Homebrew it. That's the D&D Way.

You are in fact describing an old D&D trope, made popular in the Curse of the Azure Bonds (computer game, adventure module, and novel) back in 1989. In AD&D 2e module FRC2 Curse of the Azure Bonds, PCs get these magical tattoos put on them that force their actions, and the campaign is about their attempt to escape them.

The rules for the bonds span 3 pages in the module, but as for removing them:

Dispel magic and remove curse will never have any effect on the brands, except to bring about the results mentioned above. A limited wish spell (if successfully cast without the death of the magic-user) will remove one of the marks from one individual. A full wish spell will remove up to three of the marks. Short of these actions, the Azure Bonds will prove extremely difficult to delete. Attempting to cut off the arm and regenerating it through magic will result in the brands merely reappearing on the new limb.

Anyway, if you don't want them removable by the rules, make up a new thing that someone has just created. This still leverages the rules framework, but specifies what works and what doesn't. This is basic homebrew content generation expected of any DM, and first party published adventures, monsters, etc. don't hesitate to say "well this is a curse but..." when needed.

Homebrew it. That's the D&D Way.

You are in fact describing an old D&D trope, made popular in the Curse of the Azure Bonds (computer game, adventure module, and novel) back in 1989. In AD&D 2e module FRC2 Curse of the Azure Bonds, PCs get these magical tattoos put on them that force their actions, and the campaign is about their attempt to escape them.

The rules for the bonds span 3 pages in the module, but as for removing them:

Dispel magic and remove curse will never have any effect on the brands, except to bring about the results mentioned above. A limited wish spell (if successfully cast without the death of the magic-user) will remove one of the marks from one individual. A full wish spell will remove up to three of the marks. Short of these actions, the Azure Bonds will prove extremely difficult to delete. Attempting to cut off the arm and regenerating it through magic will result in the brands merely reappearing on the new limb.

Anyway, if you don't want them removable by the rules, make up a new thing that someone has just created. This still leverages the rules framework, but specifies what works and what doesn't. This is basic homebrew content generation expected of any DM, and first party published adventures, monsters, etc. don't hesitate to say "well this is a curse but..." when needed.