From Le Vieux Lapin, who says:
Is the phrase “stick the dismount” from gymnastics? I found several instances of it on the web, ranging from a couple of gymnastics references to one in a report on the current US president. However, nothing I found explains what it means or provides enough context to do better than a slightly-educated guess. Maybe “land on your feet”?
Often with long-running and high-continuity strips, I want to write off some puzzlement at a particular episode as a matter of “Well, wait to see how it fits with the whole story”. But in this one, I think we were handed a recap right there in the dialogue.