Is there a pet relief area in the Tpa?

There is an area For pets but it is outside of the terminal.

You can use the pet relief areas across from the landside terminals the grass areas and ticketing in at baggage claims

Yes

Yes there is

Tampa International Airport (TPA) pet relief areas are located inside and outside the terminal. Relief areas for pets/service animals around the Main Terminal are located in the grassy areas across the vehicle drives of the arrival (baggage claim) and departure (ticketing) areas.