What happens if I use the Coiling Grasp Tattoo on the same target multiple times?

One of the new items in Tasha’s Cauldron of Everything is the Coiling Grasp Tattoo, a rather interesting uncommon that lets you damage and grapple enemies at range if they fail a Strength saving throw. Fascinatingly, it has no limitations on its uses – it lasts until the target successfully escapes the grapple, you move too far away from it, or, importantly here,

or if you use this tattoo on a different creature.

However, let’s picture a situation where I have a creature grappled using this tattoo, and my best course of action is to use the tattoo on the same creature again, to try and deal damage to it if it fails the saving throw. This time, however, the creature passed its saving throw…

… but I did not use the tattoo on a different creature. Am I right to assume the target is still grappled, just doesn’t take further damage this turn?