Is it safe to remove part of the drywall behind plumbing to eliminate noise?
I'm guessing you have a transitional hybrid plaster, where you have 3/8" gypsum panels behind and about the same plaster in front. This makes your wall very robust, so yes, you can carve it out a bit. Try not to go more than about 1/3 the total thickness of the wall panel as a whole, and only remove the paper facing where necessary. That's really what provides the strength with the gypsum panels. 

I would carefully cut the paper around the carving site, then use flat screwdrivers and other tools to gently dig out the gypsum as needed.

If the trough becomes substantial, you could reinforce the back side (which we see in your photo) by bonding some blocks or plywood using construction adhesive and screws to the stud alongside. I'm guessing that the contact is only at the joint hub, though, which means the carving will be small enough to not warrant reinforcement.