Call up Budget
You should really call up Budget's Customer Service line. The dollar difference is big enough for an argument, IMO. Good thing you have a hard copy of the confirmation.
You don't happen to have a Budget FastBreak number, do you? From my past experience, when I made an online reservation, and then later on, call in to have my FastBreak number added to the record, that will raise my rates, quite significant in some cases.