You would have to test on an inconspicuous area of the red fabric, but I have always used alcohol. You saturate a paper towel with the alcohol and then put more layers underneath and just blot, blot, blot until most of the ink is gone and then wash. You have to move the paper towels frequently as they absorb the ink.
Some folks have good luck with hair spray, just make sure it is the kind with alcohol in it as that is the key ingredient. I just skip that and got straight to the alcohol.