FBS inactivates Trypsin via protease inhibitors, such as α1-antitrypsin and α2-macroglobulin. Evidence is the fact that Exosome depleted FBS can also inactivate trypsin.
I would like to add that the serum proteins also serve as substrates for Trypsin protease (an enzyme). Therefore, depletion of exosomes from FBS is not likely to alter the outcome. Whether an exosome preparation alone can "inactivate" the enzyme may depend on the source of the preparation and the number of exosomes.
If you give little more detail might can help.., if you going to shave your exosome with trypsin to test for protein content or something inside, you can heat up to inactivate trypsin.
If you talking about culturing cells in FBS free medium and trying to passage with -FBS medium, there is different approach available. But need more details.. from you