As an NFT platform, what do I have to do if the owner of older rights tells me about an ENS domain that allegedly infringes its IP rights?

In case, you see a risk of infringement, it would be advisable to take precautions to flag the relevant token/ENS domain as potentially compromised. Further, you should not enable trading such a token/ENS domain on your platform. You may otherwise be liable for indirect/contributory infringement for supporting an illegal action.