Buddhist thought on Amends

I don't know, so I'll answer with the little bits I do know.

• I think that, to ordain as a monk, a person should (must) be free of debt and of good reputation -- I don't know how that's interpreted with respect to past theft.

• There are some crimes where it isn't even obvious how to "make amends" or "repay the victim" -- if you steal someone's life, for example. And yet there is at least one famous example in the suttas of a murderer becoming a monk, enlightened and harmless.

• I guess everyone has a lot of past karma -- and Buddhism may be kind of about ending karma rather than continuing to act on it -- and for that reason I sort of doubt (I might be wrong) whether he taught people to make amends by repaying victims (especially materially), but I also hesitate to say that you shouldn't.

• There's a notion of owing a great deal to one's parents, a debt which can't be repaid.

• See also topics about 'forgiveness' (for example), which might be relevant

Actually a question already often answered here, for example Confession in Buddhism

Did the Buddha address the idea of making amends for past wrongs?

Yes. It's a very important point, althought very denied by "Buddhists" and "reformer" since they sell/advertise with a pseudo liberal idea of remorse-lessness without having given causes for such.

I understand that we really only have the present moment in which karma is made, and where past karma manifests.

It's possible good to understand kamma better and that "only present" does not help much. Good, as most, Ven. Thanissaros generous Dhamma gifts: Karma Q & A

But say one was a thief in this lifetime, stole much, but then found Buddhism and the path. According to the Buddha, should this person make an attempt to repay the victims of his/her theft?

If such is possible, not always would a "victim" accept such, such can nothing but useful. It's important to understand that "nobody" would force you in regard of confessions, amends or repay from the side of the tripple Gems. How ever, as for the case one wishes to join the monastic Sangha, certain questions are raised and Monks are restricted from giving ordination to certain people.

Generally again the important story of Angulimara, the mass-murder, to get some understandings that wrong and right is not something lasting till certain points of attainings.

"No future" (for the current existence) in Dhamma are only in 6 cases, for one having killed mother, father, an Arahat, caused the Buddha shed bold, scaused a split of the Sangha and if holding strong wrong views, like those who deny the requirment of remorse, making amends of faults and other cause and effect denying ideas.

Hearing the good Dhamma, accepting right and wrong as explained and taking refuge in the Gems, if truthful, is the most usual kind of showing ones change and stick to virtue out of firm confidence.

At least: one who walks the path in it's full, is one who will "repay" all debts and an Arahat is someone really free of debts. Yet there are still three person hardly ever to repay.

(Note: this is not given for trade, exchange, stacks and what ever is thought to bind to the world for gains their but for liberation)

Walking the path with bad karma presently lingering will make it more difficult to gain wisdom. This is because the guilt you feel from stealing will distract you from your cultivation of concentration and insight. If you find you are having a hard time focusing during your meditation sessions because of this guilt, making amends could help you better progress in your search for enlightenment. If you are just suffering in general because of it, it still may be beneficial.

That being said though, it is not required to clear that karma. Once you attain enlightenment, all your karma is released, and the guilt will no longer remain.

So the answer is, how much is it bothering you? If you feel sad and guilty every day because of what you've done, making amends can relieve you of that. If it is of little concequence to you, don't worry about it and continue the path.