We took out the GFCI outlet as it kept tripping and turning off the frig in the garage. Our jetted tub stopped working (no power to the plug at all) and the outlet says GFCI protected. Do we have to put the GFCI back in to get the tub to work?
The GFCI that you removed was controlling the circuit to the jetted tub. Here's the deal: You must have GFCI protection to the tub to meet code and be safe. It is supposed to be a dedicated line - meaning that the only thing on the line is that tub. It sounds like yours was wired up so that the same circuit powered both the tub and the garage outlet.
The proper approach would be to get an electrician in to rewire so that there is a dedicated line to the tub that is GFCI protected. Then have them find another source of power to the garage. The garage also must be on a GFCI line to meet code although it's not as critical a safety issue as the circuit with the tub.
There is a possible simple solution: GFCI outlets can go bad and become too sensitive. You could try just replacing the GFCI that you removed with a new one and see what happens. Be aware that even a properly functioning GFCI can be tripped by things like lightning.