Hmm, alot of info to consider here.

I would not trust any leftover residue to be "okay" to leave, as the cleaner contained d-limonene, and would not want to risk that being left behind. And I would also prefer to not have any petroleum distillates leftover either, whether they'd be okay or not, I'd rather have a more "pure" grease in there.
Besides, I'm using a synthetic grease "Tri-flow with Teflon."

I still haven't done anything more with it yet. When I have time in the next few days, I'm going to spray it down with brake cleaner, as it is made to remove grease and oil from metal, and leaves no residue.

Thanks to everyone for their input