Can the seeds of desires bowed in the past lives can now be eradicated from the mind completely?

First of all, a seed of desire, or a seed of anger, etc. are not karmic seeds (or karmic imprints). They do not ripen in the same way at all. A seed of desire will give rise to a mind of desire. Second, desires are not seeds. The seeds are non-associated compositional factors while an instance of desire is a mind.

Yes, the seeds of the afflictions can be abandoned so that they never give rise to an afflicted mind, such as a mind of anger, lust, etc.

There are two types of abandonment:

1. Partial abandonment, and
2. Complete abandonment.

Partial abandonment is also called 'non-analytical cessation' since such an abandonment happens when you engage in Samata and the Jhanas. When you reach a concentration of the form realm (such as a mind of calm abiding, etc.) afflictions of the desire realm are abandoned, but the seeds are still there. This is a partial abandonment, since the seeds are not yet abandoned.

The way to abandon the afflictions together with their seeds is by generating wisdom directly realizing emptiness. When the wisdom directly realizing emptiness acts as an antidote, it abandons afflictions together with their seeds, this is called analytical cessation and it is complete abandonment. According to Prasangika, the first moment of a wisdom directly realizing emptiness does not abandon all afflictions altogether (and their seeds), but merely the intellectually acquired afflictions and their seeds. It is only later, when the wisdom is conjoined with an accumulation of merit (or with the six perfections) that this wisdom is strong enough to abandon innate afflictions and their seeds.

Usually, according to so-called Hinayana tenets, the seeds are abandoned by way of generating wisdom directly realizing the sixteen aspects of the four noble truths.

In any case, such a wisdom is a mind of special insight and is thus a union of calm abiding and special insight. Calm abiding must be attained first.

A seed is consciousness, not desires.

Thus kamma is the field, consciousness the seed, and craving the moisture. The consciousness of living beings hindered by ignorance & fettered by craving is established in/tuned to a middling property. Thus there is the production of renewed becoming in the future.

Bhava Sutta

Karma can only works with sense gates, no sense gates then Karma has no power.

Another straight up answer:

ariyo (noble) aṭṭhaṅgiko maggo (eight fold path) kārma-nirodha (extinction of karma) -gāminī (goal) paṭipadā (mode of progress)

Practicing noble eight fold path is a mode of progress to end karma.

This comes from the Nibbedhika Sutta (AN 6.63):

Katamo ca, bhikkhave, kammānaṃ nidāna-sambhavo? Phasso, bhikkhave, kammānaṃ nidāna-sambhavo.

And what is the cause by which kamma comes into play? Contact is the cause by which kamma comes into play.

And:

Katamo ca, bhikkhave, kamma-nirodho? Phassa-nirodho, bhikkhave, kamma-nirodho. Ayameva ariyo aṭṭhaṅgiko maggo kamma-nirodha-gāminī paṭipadā, seyyathidaṃ: sammā-diṭṭhi, sammā-saṅkappo, sammā-vācā, sammā-kammanto, sammā-ājīvo, sammā-vāyāmo, sammā-sati, sammā-samādhi.

And what is the cessation of kamma? From the cessation of contact is the cessation of kamma; and just this noble eightfold path — right view, right resolve, right speech, right action, right livelihood, right effort, right mindfulness, right concentration — is the path of practice leading to the cessation of kamma.

So karma has Phassa ("detection" or "contact") as its Nidhana Sambhava (which I translate as "stage where karma plays out", or which buddha-vacana.org translates as "cause by which kamma comes into play"). Without stage to play, karma is powerless. Reference "dependent origination" to find out how Phassa or detections end.