Wiktionary has UK slang definition of rocket of "A severe reprimand; a telling-off."

I found quotes for "put a rocket up" that suggest it is UK slang. And pretty common since BBC has article for "How women students put a rocket up Cambridge".

I assumed it meant "put a rocket up their ass", a clever SpaceX-themed play on the phrase "put a boot up/in their ass".

Sort of "Poke with a stick". Some contractors are filing leans against SpaceX assets in hopes of getting money owed.