Amaranth are susceptible to leaf miner damage, which is what I can observe with your plant.

Hmm, looking into it, it does kind of look like that. What's the best way of treating it, do you think?

Squish them. Pinch the end of the mines or the lumps. The only other way besides discarding all the affected leaves would be a systemic insecticide which most of us do not condone.

Hahah, that did it! I got a pair of pliers and squeezed the little blighters into oblivion. I've learned something about Amaranth care today. Thanks, taz.

You're welcome pro!