I'd remove the white plastic. I grow gourds on the ground all the time with no problem. You're in zone 5 and I hear the temps. are already getting into the 30s at night. You may not be able to harvest these gourds unless they're already drying. Good luck.

I also live in zone 5, my gourd garden is in Hesperia Mi. area. Around the middle of Septemberwe got a light 2 night frost. Pats of the gourds that were not under the leaves got frosted. the skin feels slippery & peels when you touch it. The gourds were harvested last week & are just fine & have started the drying process.Maybe this is what is going on with yours. Good luck. Lois