don't you usually say, 对不起 for I'm sorry?
They both mean "I'm sorry" but Duolingo has the two mixed up! 对不起 is correct here but Duolingo won't take it (not in the word bank, won't accept it typed).
Can you use 过错 here?
I interpret this literally as "I'm sorry, my bad" (it is my bad)
Could you remove the 的 here with it still being correct?