I just bought a new house and I need to re do 2 bathrooms that have a gray tile around the 3 shower walls, so I was wanting to know if I could tile over them with the smaller tiles with the mesh backing?

No, I do not believe that the adhesive will bond to the old tile.

It would be wise to take it all down and replace the walls and tile at the same time. More work, but you will have a better looking job in the end. To tile over old tiles is not advised. The walls may not be sound underneath the old tiles.