You should absolutely contact the TA and ask them to fix this. But you may not be able to get them to change it and in that case you will need to keep your boarding passes and submit them to UA for credit.

I've had this sort of thing happen and mileage credit was the least of my problems. A travel agent that our custmer insisted we use to book travel appended my middle name to my last name. So my name was something like FIRSTNAME MXYZZY. They absolutely refused to fix it because the characters were all correct -- they were just in the wrong fields -- and they were sure I could fly (and I did).. Because of this, though, I had no status for purposes of going through security, boarding, etc. Good luck!