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Even if the belt was split right there on the line, the strength of the now two belts combined would be about the same as the original belt. While replacing it would be "a good idea," I don't think it's really critical. A cut 90 degrees to that one, yeah, replace it today. And make sure nothing is still rubbing it.
Not saying this is the original posters problem, but thought I would share:
Reminds of a time I was wrenching on my bike, dropped a simple 1/4 bolt. When wrenching, if I drop a bolt. nut, washer, whatever, I listen for the sound of it hitting the ground. Could not find that bolt anywhere and did not hear the "hit the ground sound".
It was a simple bolt, so grabbed another and finished the project. Took bike out for a ride, and bike was not up shifting. Looked at the foot shifter and ta da! Bolt fell right in between shifter and outer primary just perfectly. The shifter would go from neutral to first, but no up shifting. The bolt wedged in there perfectly. Lessen learned.
Always look for that lost bolt! Till it drives you crazy and you use every cuss word in the book to help find it.
From the picture the scratch is just cosmetic. Replace it if it'll make you feel better, I wouldn't.
JMO
Like suggested, a piece of painters tape in a few spots will tell you if the offending object is still there.
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