Should I pay Apartment Carpet Burns Penalty?

That is a hard question but since you did not have it written down when you did your move in inspection sheet you are more then likely going to have to pay the bill. It sucks but you really need to keep track of the stuff when you move in and out. I take notes and pictures of things so that way they can not say that I damaged anything or charge me for repairs that were not mine. Write this one off as a bad learning experence. Also the collections agency will sue you and you will then end up paying court fees as well as the original amount.