The painted border is crisp, but the paper lifts with the masking tape. The problem appears at the end, when it is tempting to pull faster and finish. A small test at the beginning can make this moment much less uncertain.
Use tape intended for the material and task. Household tapes differ in adhesive strength, and paper varies in surface, thickness and coating. Low tack is a useful description to investigate, not a guarantee that every sheet will release cleanly.
Test the whole combination
Use an offcut of the same paper with the same paint or ink. Apply a short strip, complete the relevant steps and remove it at the time recommended for those materials. A test on clean paper alone does not show how the surface behaves after it has been painted.
Press only as much as the task needs, following the tape instructions. Avoid repeatedly burnishing a delicate surface because one edge looks uncertain. If paint can run under the tape, improve the application method rather than compensating with excessive pressure.
Slow down when resistance changes
Support the sheet on a flat surface and peel carefully, keeping the tape close to the paper rather than yanking upwards. Stop if fibres begin to lift. Do not add heat, solvent or water to a finished piece without knowing how every material will respond.
For an important original, a damaged test strip is useful information: choose a different masking method, paper or design before repeating the problem on the artwork. A border made with a removable paper guide may suit some projects better than adhesive tape.
Keep the successful tape brand and paper combination in your craft notes, including how long the tape remained in place. The aim is not one universal trick for removing tape. It is a repeatable method that respects the surface you are trying to preserve.