Smudge / smear that is very hard to wash off

What is the name (noun or adjective) for a smudge that is very difficult to wash off the surface?

Example:

I tried to wash this ______ off my shirt, but it seems to be too ________ to remove

You can call it a stubborn stain.

stubborn adjective 1.1 Difficult to move, remove, or cure. ‘the removal of stubborn screws’ - ODO

Your example would then look like:

• I tried to wash this stain off my shirt, but it seems to be too stubborn to remove.

I tried to wash this stain off my shirt, but it seems to be too stubborn to remove.

Tough is used referring to stains which are difficult to remove:

very difficult to do or deal with. (M-W)

Usage examples:

From Clean your house from A to Z:

Grass is a tough stain, one that is especially common on the knees of children's jeans.

From Country living:

TM OxyKIC combines an oxygen-activated cleaner with a tough stain fighter in one easy-to-use spray.

From Clean it fast, clean it right:

Oil is a tough stain, plus it is like a magnet for dirt. Remove oil stains as quickly as possible.