I'm also having this issue. I swear I saw a thread somewhere describing how to fix it a few days ago but I cannot find it for the life of me. (No not the Captian Sim 777 thread).
Whenever I push back in any of the PMDG 777s, the nosewheel slightly sinks into the ground. When the tug is released, it suddenly pops back up. I was going to take a screenshot of it but that just happened to crash my sim.

EDIT: I figured out where I saw the fix. It was in the GSX Community discord in the support-general channel. Someone said that its caused by FSRealistic and to turn it off during pushback. I'm going to try that my next pushback and update this accordingly.