I run into this all of the time when I am cleaning carpets in Las Vegas! Red stains are usually indicative of a red food dye. Dyes of any type are permanent by nature and therefore very difficult to remove.
Difficult yes, impossible no. Now please I will assume no responsibility if you do not follow my directions. This post is meant to be informative and helpful but unfortunately not fool proof.
In the 20 plus years I have been cleaning carpet I have messed up once on a beautiful green carpet. I was too aggressive and pulled a little of the yellow out and was left with an impressive blue spot. So please be aware that problems can and do arise on occasion. So please follow my advice carefully.
Here is how we do it.
Start by taking a mixture of clear ammonia and water. You want to make sure you are using clear ammonia not the yellow stuff with detergent in it. I also recommend distilled water, but to be frank regular tap water will work. Combine the 2 half and half in a trigger spray bottle.
Next spray this mixture onto the red spot trying to avoid the carpet that is not dyed red. You can get the carpet fairly wet it will be ok.
Now take a damp white cotton towel and place this over the red spot with the ammonia and water mixture on it. Please make sure that you are using a white towel. A green towel or may bleed green dye into your red spot, a blue towel may bleed blue dye. etc.
Follow this with a steam iron set to high steam. Place this on the red spot for about 45 to 60 seconds. The steam and water/ammonia mixture releases the hold the dye has on the carpet and draws it up into the towel. You may need to do this 3 or 4 times to get the maximum results. Make sure you pay attention to the carpet and look for signs of the original color lightening up. If you see any sign of this I advise you stop immediately.
Once you have removed as much of the red as possible. Flush the spot with clear water and remove as much this water as possible with a wet/cry vacuum or your Bissell type carpet cleaning machine. Next take a towel and blot up the remaining water. I like to fold up a bath towel and simply step on it. Then flip it over and do it again. After you have blotted up as much water as possible simply set a fan on that area to help it dry more quickly.
And you are back outside sipping lemonade dreaming of sunsets on the beach in no time! Just remember to clean your carpets annualy.