I've been having this problem and it's been bugging me. Every time I vibrato with my first finger on the D string somehow the G makes a sound (vibrato pulling down). I don't know how to mute it because I can't use the palm because it'll end up muting the string I'm playing. This only happens when I use the first finger.
you can rest the middlefinger of your picking hand on the G string and still pick with the plectrum between your thumb and index on the D.