Question

The Rabbi said in a lecture on memory at Bar-Ilan that memory is essentially leaving a part of the person with me, and my question is: how can it be that the Torah commands us not to leave any trace whatsoever of Amalek, while at the same time commanding us to remember him? After all, something is still being left behind. Especially according to what Rashi said, that absolutely nothing should remain—that people should not be able to say, “This is a donkey that once belonged to Amalek.” I assume the simple explanation in the Torah is that the obligation is to destroy all the physical remnants of Amalek. The question is whether there is nevertheless some tension here, and if so, whether it is expressed in some way? Thanks!