I am in a similar but not identical situation myself so thought I'd provide some details on my experience. I haven't had any issues with the discrepancy albeit I applied for Global Entry prior to marriage and actually prior to issuance of my Green Card.

I had a UK passport in my original surname. I applied for Global entry in my original surname too, as Global Entry was available to UK citizens entering on the Visa Waiver Program. I've got my Green card now which is now in my married name. I had no problem updating my Global entry to use my Green card and my married name, nor have I had problems with my UK passport being in my original surname. I carry my marriage certificate showing the link between my UK passport (unmarried surname) and my Green card/Global entry (married surname) should anybody need it. However, I've never been asked for it.

I have about 5 years left on my UK passport so I've seen no major need to update it, and I'm still about 4 years away from applying from US Citizenship.

In summary, my situation is:
- UK passport with birth surname
- Green card with married surname.
- Global entry now with married surname, but applied/approved with original surname. Went to a Global Entry enrolment centre to change it after marriage and issuance of green card.

I doubt that either USCIS and CBP will have any issues with the differences in name.