Pink Clothing Dye Transferred to White Jacket?

I borrowed my sister's white Omni-Shield Colombia jacket. The day before she wanted it returned, I had thrown it in the washer with other white articles of clothing, along with a bright pink wash cloth I failed to notice. I tried bleaching it out, tried a stain remover, and I tried Rit Dye Remover. Nothing worked, although the Rit Dye Remover did lighten the pink up. So instead of the jacket having bright pink blotches all over, it now has pale pink blotches.

The tag on the jacket reads; "Machine wash cold Permanent press, Powdered detergent, Rinse thoroughly, Wash separately, Do not bleach, Tumble dry permanent press low, Iron low, Do not use fabric softener, Do not dry clean. Shell: 100% Polyester, Lining: 100% Nylon, Mesh lining: 57% Recycled Polyester, 43% Polyester Exclusive of trimming"

I don't know what to do to get the jacket back to white, if anyone has any suggestions, tips, tricks, secret methods, anything that could possibly work, please let me know.

By Sadie