I agree with Grant.
But also, in a general sense:
-"to forget it" means "to not remember it."
-"to forget about it" means "to not think about it" or "to not worry about it" or "to not be bothered by it"
I might "forget about" the fight we had last night. But, unless I was somehow impaired, I will probably not "forget it" any time soon.
As illustrated in Grant's examples, these are not strict rules, and both statements are sometimes used when the other would seem to be more appropriate.