Even with the vent cover, my vent lid got brittle and cracked in 4 years. Yes, the TT is covered for winter.
So I replaced the whole cover. Cheapest on Amazon was about $22 each but I found a twofer for $30 so now I have a spare ;) Replacement is black, I like it dark to sleep. Between that black cover and my reflectix window covers, nap time is much easier!
I think I have the same MaxxAir cover as you, it went from white to yellow in two years. I took it off & spray painted it white again. Couldn’t get well around the vent filter, though ;(
You really should replace that stock fan with a full size one. Then you can really move some air.
