Assume you're grappled but you have a melee attack that can cause the paralyzed condition. If you successfully paralyze your grappler, will that break the grapple? Paralysis causes someone to be incapacitated which prevents them from taking actions or reactions, but resisting an attempt to break the grapple (in a contested roll) doesn't require either of these from the grappler.
Is the answer different if the grappler is using the Coiling Grasp Tattoo? In this case, the grappled creature can try to escape using an appropriate check, but it's not a contested roll, so the tattoo's ability to maintain a grapple seems unaffected by its host's paralysis.