„Poduchy” in your example sentence is an accusative plural of the word „poducha”, which is an augmentative variant of „poduszka”. Unfortunately, with few exceptions, diminutives and augmentatives are not accepted on the course. Polish can create them out of tons of words and adding them to the course would be a ton of work.
„Pod uszka”, if you want to be technical – if the word would come from ucho (and not the diminutive), it would be „poduszyka” – „ucho” has highly irregular plural, because it has partially retained the ancient as eff ( :P), dual, which is otherwise completely gone from Polish. ;)
Well, in a word evolution there can be many changes that can change words to be easier to pronounce. „Poduszka” from „pod uszy” is a "folk ethymology"; one that sounds plausible, but is actually wrong. According to Katarzyna Kłosińska, it comes from the word „podmuchać”, because for people pillows felt like they were inflated.