Medicine cabinet installation help

I installed a surface mount medicine cabinet over the weekend. It came with metal side brackets that come with removable backing to adhere to the side mirror. The problem is the screw hole for the bracket (into the cabinet) was too small, and by screwing hard into the bracket I apparently stripped the hole. The bracket is now loose against the cabinet and I can't get the screw out. Will the weight of the mirror hold it tight? Or does anyone have an idea for how I can get the screw out? It's step 11 in these directions - https://www.us.kohler.com/webassets/kpna/catalog/pdf/en/1133135_2.pdf

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