I can't help you directly, as I don't know what an original '37 GMC COE would have regarding the handles for the windshield regulators. Apparently, there are two separate regulators for the split windshield, unlike the 1/2 ton trucks which have a single piece of flat glass and only one regulator. I can tell you that my '37 Chevy and '42 Chevy half ton trucks have a bolt or nut connecting to the center of the spline, easily noted at the hub of the handles. My Diamond T has a similar arrangement of the the handles for the two regulators for it's split windshield.
From looking at your picture a previous owner may have glued a handle to the splines of your regulator. I hope that is not the case but if it isn't obvious how to remove the handle, that is a likely possibility. Assuming that is true, perhaps judicious use of a propane torch to the junction of the handle and spline may soften the adhesive enough to pull off the handle.
Kent
Last edited by Lightholder's Dad; 09/22/2021 8:06 PM.