No-Toil is a great product. The cleaner, oil and rim grease are biodegradable so you can clean your filter in the kitchen sink.
I think I read that somewhere recently!
In direct response to the question, it would be most effective to have zero solvent in the filter before re-oiling. Solvent being a more refined product than the oil it is supposed to remove, there's a better chance of soap&water getting IT out.
But, NoToil is the ONLY way to go.
I read that somewheres, too...........