The stain problem is mostly caused by the dried paint coming to the image part of the cliché. Causes and solutions:
Causes of Tampon

If the pad is too flat, a more tapered pad should be used.
If the bumper is worn and rough, the bumper should be replaced.

Causes of Cliché

In case the cliché depth is not sufficient, a deeper cliché should be prepared and printed.
If a wrong type raster is applied to the cliché, a cliché with a suitable raster should be prepared.

Causes of Ink

If the ink dries in the cliché cavities, it should be cleaned with cliché thinner.
If the ink is too thick, thinner should be added.

Material-Related Causes

The material may be contaminated with oil: the material surface should be cleaned with alcohol.

Other Reasons

If the printing speed of the machine is low, the printing speed should be increased.