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...... if the scratch is deep (say about 1/2 thickness or close) , and if it's in an area that will be subjected to regular flexing (like the bottom) ... then it's probably a good idea to reinforce and/or plastic weld fill it back up .
Welding as discribed already is the standard precautionary for bad (deep) scratches .
A reinforcement patch on the inside is a layer of fiberglass cloth and resin mix . G-Flex always has good reviews on poly . Light sand and flame the surface for best adhesion before apply a patch .
The plastic has become thinner in the deep scratch , constant flexing , extra wear , some brittleness with time can cause it to crack through . Fixing it now is probably better than later after a full crack through .
There's some here who have done the welding many ways and many times , maybe they'll kick in .
I've never owned a single layer polyethylene , so have never had to fix one , but they do it all the time .
..... if you're NOT concerned the deep scratch (gouge) is in an area that might crack later from flexing , then a cosmetic fill is all you want . Melting a poly tarp to fill with is a cosmetic not a structural .
You could just as well heat the putty knife and re-smooth with the putty knife and scraper for cosmetic .