I had a tarp folded up for several years. It may be the one in the picture but I'm not sure. Anyway, it was just a but smaller than the cargo cover for the M35 but about the same weight. When I unfolded it, I made ear wigs and spiders and centipedes and critters like that homeless.
I spread the tarp out, sprayed it with bleach and scrubbed it. It didn't take long but made one huckava difference. None of the displaced critters wanted to come back.
So, then I had a stinky tarp. I spread it out so that air could circulate over and under the tarp to take the smell away. That took a bit longer than scrubbing it but it worked. If you don't have the space to spread your tarp out, put it back on the truck but don't tie it down. Instead, use some sticks or whatever you can find to spread the tarp out. I use cheap 1/2 inch diameter PVC pipe. I cut a notch into one end that the rubber straps that are supposed to secure the tarp to the truck fit into. The other end I just lean against the truck so that the tarp is spread out and wind can blow over the truck and through the truck. The PVC may flex a little in the wind but it won't break. If you cut a 10 foot pipe in half, you get two 5 foot "tarp holders". You probably want at least eight (three per side + two in the back). So buy four 10-foot pipes.
Afterwards, you can give the "tarp holders" to your kids or grandkids. They will convert them to Star Wars light swords or find some other use for them.