That depends on if and what kind of wood is under that primer. Sand a small section and investigate. Better yet ask your contractor who installed them for the specifications and look it up. There is a good chance it is not wood under the primer. Another option if it is not wood is to have a faux finisher come in and make the windows look like wood for you.

It is Pine underneath and that is what we wanted.

Then I would have a professional come and remove the primer and refinish:)

In many cases, paint grade wood is lower quality wood and/or finger jointed (made up of many small pieces). If... this is the case, it will look terrible stained and finished.

what a PIA. Thank you for letting me know.