I have not come across information linking GLP drugs to kidney problems except in one narrow scenario. In most cases they actually slow kidney decline, improve function, and lower protein in urine. The only time stopping is advised is when severe vomiting or diarrhea from side effects or overdose leads to dehydration and acute kidney issues. Overall this does not seem like reliable medical guidance.
Perhaps the better approach is to pay closer attention to fluid intake rather than missing doses. It comes across as bad guidance to recommend stopping the medication when simply drinking more water would address the concern.