My experience with food dye and carpet isn't great, but I'll tell you what I know.
When I asked, Rouge suggested trying club soda and blotting with a sanitary pad as it absorbs the moisture and hopefully remove the stain. But We had red food dye and it is the hardest colour to get out. I had a professional come in and try to get the stain out, but ultimately we had to replace the patch of carpet where she spilt it.
if it helps your own peace of mind, some agents arnt as "fussed" if it is a legit accident from a child, my last agent turned a blind eye to my 3yo's "mural" on his bedroom wall, but the one befor that took me to the rental tribunal when he bent a vanetion blind, only to be told by the judge what do you expect in a childs room.
good luck.
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