This is a very interesting problem. Looking up the definition of scrooge, I find many references to the Charles Dickens story "A Christmas Carol", where the main character is named Ebenezer Scrooge, who is a selfish person who is unwilling to give or spend.
Scrooge, as a noun, is used to describe someone who has similar characteristics as the aforementioned character, but you ask about scrooge in the form of a verb.
Looking for it online (using "he scrooged") gives me a lot of pages about the Wind in the Willows, which makes me think it's a phrase coined by the author of this book. If I would have to guess, in this context, it can mean, taking something with all your might, wanting to have something desperately. But that's just a guess.
Student or Learner