Re: Please need letter correction
Yikes! Don't mention their apology at all! You're the one making a request, and their apologies are just part of being polite. By starting off "accepthing their apologies" you risk sounding like you think you're superior to them, but lowering yourself a bit to interact with tem.
Simply start by thanking them for getting back to you.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.