Did ancient Germans take pride in leaving the land untouched?

Unless specified further it seems quite contestable that Caesar wrote much to this effect.

If any ancient Roman author comes to mind, with sufficient detail, then it is primarily Publius Cornelius Tacitus, namely with his Germania.

In that account we find some descriptions that come a bit closer to "not touching land":

Baduhennna is solely attested by Tacitus's Annals where Tacitus records that a grove in ancient Frisia was dedicated to her, and that near this grove 900 Roman soldiers were killed in 28 CE. Scholars have analyzed the name of the goddess and linked the figure to the Germanic Matres and Matronae.

Soon afterwards it was ascertained from deserters that nine hundred Romans had been cut to pieces in a wood called Baduhenna, after prolonging the fight to the next day, and that another body of four hundred, which had taken possession of the house of one Cruptorix, once a soldier in our pay, fearing betrayal, had perished by mutual slaughter. 74. The Frisian name thus became famous in Germany, and Tiberius kept our losses a secret, not wishing to entrust any one with the war.
WP: Baduhenna

They were helped by a night of bright starlight, reached the villages of the Marsi, and threw their pickets round the enemy, who even then were stretched on beds or at their tables, without the least fear, or any sentries before their camp, so complete was their careless and disorder; and of war indeed there was no apprehension. Peace it certainly was not—merely the languid and heedless ease of half-intoxicated people. 51. Cæsar, to spread devastation more widely, divided his eager legions into four columns, and ravaged a space of fifty miles with fire and sword. Neither sex nor age moved his compassion. Everything, sacred or profane, the temple too of Tamfana, as they called it, the special resort of all those tribes, was levelled to the ground. There was not a wound among our soldiers, who cut down a half asleep, an unarmed, or a straggling foe. The Bructeri, Tubantes, and Usipetes, were roused by this slaughter, and beset the forest passes through which the army had to return

Since fana is Latin for "temples," it has been suggested that it was a temple to a god Tan, shortened from the German word for a pine-tree, Tanne, or that the first element meant "collective."
WP: Tamfana

These are both allusions to the concept of sacred groves that were still in higher currency at the time in Germania when in Roman and Greek lands this concept has 'lost some ground' or popularity. Equally "the land" might be a something like Nerthus or 'Mother Earth'. These woods being 'holy' were then unlikely to be used for agriculture.

There is nothing especially noteworthy about these states individually, but they are distinguished by a common worship of Nerthus, that is, Mother Earth, and believe that she intervenes in human affairs and rides through their peoples. There is a sacred grove on an island in the Ocean, in which there is a consecrated chariot, draped with a cloth, which the priest alone may touch. He perceives the presence of the goddess in the innermost shrine and with great reverence escorts her in her chariot, which is drawn by female cattle.
Germ 40 (p58)

And some special trees even had a heightened significance, and were later called Irminsul (probably):

In Tacitus' Germania, the author mentions rumors of what he describes as "Pillars of Hercules" in land inhabited by the Frisii that had yet to be explored. Tacitus adds that these pillars exist either because Hercules actually did go there or because the Romans have agreed to ascribe all marvels anywhere to Hercules' credit. Tacitus states that while Drusus Germanicus was daring in his campaigns against the Germanic tribes, he was unable to reach this region, and that subsequently no one had yet made the attempt. Connections have been proposed between these "Pillars of Hercules" and later accounts of the Irminsuls. Hercules was probably frequently identified with Thor by the Romans due to the practice of interpretatio romana.

Adding to the uncertainty present in the question itself, both authors, Caesar and Tacitus are not overly reliable in their accounts of Germanic tribes and people. Therefore the question "Did ancient Germans take pride in leaving the land untouched?" cannot be answered reliably by relying on Roman authors. What can be stated is what they wrote and how they described it. And that might be quite removed from what went on East of the Rhine.

In any case, even the above would suffice in generous interpretation only to sustain that certain designated areas were not to be touched. A general "leaving land untouched" is just incompatible with human activity. That counts as a double if that activity involves drinking beer, for which you need grain.

The practice of lending out capital and stretching it out into interest is unknown: ignorance is a surer protection than any prohibition. Lands are occupied by the whole people to be cultivated, the quantity determined by the number of cultivators. They then divide the lands out among themselves according to rank. The great extent of the land makes the division easy. They plough different fields every year and there is still spare land available. In fact, however, for all that their land is fertile and extensive, they make no effort to work at planting orchards, fencing off pasturage, or irrigating gardens. Their only demand on the soil is for corn. Hence even the year itself is not divided up into as many seasons: winter, spring, and summer they understand and have names for, the name of autumn is completely unknown, as are its blessings.

Germ 26 (p50)

Towards the north it falls back with a huge bend, and here first of all is the people of the Chauci. Although they start next to the Frisii and occupy part of the coast, they also stretch out along the flanks of all the states that I have described, and finally curve back towards the Chatti. This vast tract of land is not merely held by the Chauci but filled by them too. They are the noblest people among the Germans and one that prefers to maintain its greatness by righteous dealing. Free from greed and from ungovernable passion, they live in peaceful seclusion; they provoke no wars and do not engage in raids for plunder or brigandage. The principal proof of their excellence and their strength is that they do not rely on damaging others to maintain their superior position.

Germ 35 (p55) Sometimes "free from" is translated as 'untouched'

Germ = Anthony R. Birley (Translator): "Tacitus, Agricola and Germany", Oxford World’s Classics, Oxford University Press:Oxford, New York, 1999.