How does a thermoelectric generator generates electricity?
It converts some (a small fraction) of the heat flow to electricity. It absorbs X amount of heat from the hot side, and rejects X-delta amount to the cold side. The output voltage is related to the temperature difference between the hot and cold sides. The output current is related to delta, the heat flow difference.

Because present devices are very inefficient, without taking very careful measurements, measurements that are beyond most hobbyists to do accurately, it would be easy to conclude that it doesn't consume any heat at all. X-delta is very similar in magnitude to X. A small difference between two big measurements has been the bane of experimenters since antiquity!

So people that say 'it converts heat flow to electricity', or 'it converts heat to electricity', are both correct, up to a hand-wavy approximation. It needs both.