Make sure your LORs are signed on the back by the person that has written them and they have the address of the person on the front. I don't really think it matters who sends them in the mail as long as you don't look at them.
HAHAH yeah right....if I am sitting home with my LORs in my hand, better believe I will read them bad boys. No one but me will know I read them basically.
Are the letters enveloped already? If so why didn't the writer just mail it out him/herself?
Anyway like Dana said, have them sign the back (by the seal), especially if you are using a regular white envelope with no school name printed on it.