Vaccinations are supposed to prevent disease, in theory, and they are not designed to "help" after an exposure. The TIG would, in theory, help (though that is also debateable) if one was exposed to tetanus, but a vaccination would be worthless.
I would ask you stepson's mom if the wound bled at all. If it did, no worries at all. If it didn't, she should clean it with hydrogen peroxide.
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