Topical medication for scabies should NOT affect ink from tattoos.
The most common medication prescribed for scabies is known as permethrin 5% (Elimite) cream. It is active against many different kinds of bugs and pests including lice, ticks and the mites that cause scabies. It works by affecting the nerve function of these critters causing paralysis and death. In terms of administration, you want to thoroughly massage the permethrin cream into your skin from your head to the soles of the feet, even areas that are covered by tattoos. It should be applied in the evening before bed and removed by washing after 8—14 hours. Less than 2% of the drug is actually absorbed into your skin. While there are some reports of skin irritation/rashes with the product, it is not common and again will not cause any lasting damage to tattooed areas. The ink in tattoos lies under the epidermis layer of your skin and the Permethrin cream does not penetrate this area in high concentrations. The small amount of drug that does penetrate the skin does not cause any lasting dermatological effects.
Another less common medication for scabies is known as Lindane. This is slightly more toxic but again would not cause any lasting dermatological issues.
Just to be sure there isn't any information out there regarding cases of tattoo alterations with scabies medication, we ran a search through thousands of studies regarding agents for scabies and we came up with nothing. You should feel safe that there will be no lasting negative consequence to your skin.
Just as an FYI as well, the mites that cause scabies typically don't leave lasting scars that would affect the look of tattoos either. During an active infection, they burrow only into the top layer of the skin, much higher than where tattoo ink would be.