No it won’t. Induction stove tops are ceramic. Ceramic on mohs scale is “hard as fuck”.
Unless you have rocks (or salt crystals) stuck in the seasoning, neither polymerized oil nor any metal is hard enough to scratch it. They literally can’t.
That would be like a metal knife scratching a glass cutting board, which famously can’t happen, and is the reason why glass cutting boards are a terrible, knife destroying, idea.