Easter egg dye is vegetable based dye, and will be sensitive to oxygenated cleaner/bleach. Which usually means hydrogen peroxide base. The challenge becomes has the dye penetrated the wood pores, or the stain only absorbed into the finish?
+1 oxalic acid.
+1 It the flooring is newer type with UV cure poly, surprised you can't float the color out of the finish.
Might try alcohol to help remove the residual oils that can absorb the dye and help it lock into finish or wood. Anything stronger might melt or alter the finish.
Wife claims she uses whitening tooth paste to remove Easter egg dye from skin and some clothes. It has a mild abrasive to help remove top layer of skin with dye in it. It can be aggressive abrasive, so go easy or might leave a faded white spot where you scrub. She used same tooth paste to remove some red nail polish residue from a wood floor once. If floor finish is gloss, tooth paste will remove the sheen, and make it matte finish. Will have to wax floor to even out the sheen.
Best Luck.