Barring special arrangements, you will not be able to go airside in T3 to visit either the Tryp transit hotel or any of the lounges upon arrival. T3 is for international flights only, and you will need to pass Brazilian exit immigration and have a BP for a same-day departing int'l flight in order to going airside there.
If anyone in your party has an AA Admirals Club membership, you could pre-arrange a meeting at the business facilities in the new and very nice T3 AA lounge (you'll get gate passes at the AA check-in counter and an escort. The lounge is new and has showers that are larger than the rooms at the Saviero in T2).

T3 to T2 is a ten-minute walk or a (free) five-minute inter-terminal bus ride away. The terminals are adjacent to each other.

However, the rooms and bathrooms at the Saviero "Fast Sleep" are extremely tiny (bunk beds), and the walls are paper-thin. Not what I'd use for a business telecon.
I would get a day room at the GRU Pullman, which is a 5min. shuttle bus ride away and MUCH nicer (cost should be about 70 EUR).