To hit on or have sex with. To grinch on someone is to find them attractive for animalistic intentions. A name or future date is not necessary for the act of "grinching" to occur but may follow if the grinching was successful for both parties
Tarra: Hey Look at the hot piece of man meat
, I'm going to go grinch
Ann: Oooh girl you go get that!
Morgan: My boyfriend and I grinched all night last night!
Corey: Hey man you never came home last night what happened to you?
Adam: I was gettin my grinch on!