I GWd two old credit cards asking to remove one 30 day late, each. Basically you just state who you are, what you're asking for, give a little sob story, and plead for their help.
They will not pull your report.
If they agree to the GW, they will make the change in their system. This does not mean that they'll immediately send something to the CRAs, they may just wait for their system to update CRAs as they would regularly each month.
On the other hand, they may just ignore your request completely or send you back something denying your request.
OR they may discover something else that isn't reporting, and report that. That would negatively affect your scores.
It rarely hurts to GW, espcially if you know there's nothing else out there that the creditor can do to your report to make it worse.
Good luck!