The good news is that most modern induction cooktops are designed with safety features that prevent scratches and damage from cast iron cookware. These features include ceramic or glass surfaces that are resistant to scratches and heat. So, if you're using a high-quality induction cooktop and a well-maintained cast iron pan, you're unlikely to experience any issues.
However, it's still possible to scratch or damage your induction cooktop if you're not careful. For example, if you're using a rough or abrasive cast iron pan, it could potentially scratch the surface of your cooktop. But don't worry, there are ways to prevent this from happening. Simply make sure to clean and dry your cast iron pan before using it on your induction cooktop, and always handle it with care.