Try mixing up a solution of white distilled vinegar and water. Use one part vinegar and three parts water and put it into a spray bottle. Mist the solution on the spot and let it sit for a few seconds. Blot it up with a plain cotton towel and repeat if necessary. Resist the urge to rub th spot. Just blot it. Here is a link that might be useful: carpet and upholstery cleaners

I have to tell you how I just camouflaged a bleach spot on my light tan carpet. It wasn't a bad spot but we are trying to sell our house and every little thing makes it harder to sell. I tried everything. Coffee, tea. None of them worked. I even paid $100 for the kit that comes with a neutralizer and the different spray bottles of stuff that is supposed to bring it back to a natural color. That actually made it worse. So, I bought some water based poster paint. Using my fingers and lots of water... I worked in white and got rid of the garish yellow and pink. It took patience and time, probably two hours. I let that dry. It was all gone but it was lighter than the rest of the carpet. Actually it would have been ok. Then I mixed up some black, brown and white and very lightly I brushed through the carpet using lots of water and I got the carpet to blend in with the surrounding area. It look great. I will not be shampooing that carpet again.

For a long time with my old TL (that's supposed to be so inferior to European-style FL), I get excellent results with all my laundry and stain removal by soaking in oxygen bleach (OxiClean). This required active participation: I would start the hot water flow into the machine, add the oxi, add detergent (enzyme-based Kirkland Free & Clear), switch to warm if required to be easier on fabrics (stayed with hot for whites). Then I'd let the clothes soak for at least 60 minutes, sometimes several hours or overnight. This soak eliminated most stains without pretreating. One important exception is oily/greasy stains. Oxi doesn't do well with those. Straight detergent on the stain, Shout Advanced, or citrus degreaser pretreatment is needed for oily stains. I learned about the soak technique from Cook's Illustrated when they did their test of stain removers. Any organic, plant-based color stain, I think of oxi soak to remove it. Over the years, though, my favorite white towels and tank tops harbor faint stain residues that accumulate till the items don't look good. Inspired by the book "Home Comforts" by Cheryl Mendelson, I soaked my beloved Champion tanks in Clorox, at the correct dilution, then hung them in the sun. They looked like new. Lesson learned: there is nothing like true bleach. A few days ago, I bought a FL and tried the "Sanitize" cycle on stained white towels and T-shirts, and after nearly 3 hours was highly disappointed that many stains remained. So I still think soaking in oxi is more effective than a long, hot wash cycle in FL. A long warm oxi soak is also gentler on the spandex fabric than either super-high temperature or chlorine bleach. So my overall strategy is to oxi soak every wash in warm/hot water, chlorine bleach soak occasionally as needed. My detergent contains no optical brighteners, but those certainly make a huge difference in making whites look white. I read where people talk about how they're not "really" white because it's just an "illusion." This is nonsense. The only thing that MATTERS is how the color LOOKS to your eye/brain perceptual system. Garments that have lots of optical brighteners look great. Old garments whose optical brighteners have deteriorated look lousy, no matter how clean they are. I can see the amount of optical brighteners using a UV light. So to the OP's problem, removing stains without pretreating, soaking in oxygen bleach is the best solution I know, but if the stain has an oily component, you must either pretreat with enzyme/surfactant or use a very strong detergent. If skin can't tolerate those cleaners, I can't see any way to have stain-free clothes, because I have tried tons of different things. I would therefore recommend diet/supplements to improve skin's barrier function. I have friends with reactive skin like this, that improved greatly with more protein and EFAs (fish oil) in their diets, plus B vitamins and chelated minerals. A formula of chelated magnesium, zinc, selenium, chronium, and vanadium, makes a HUGE difference in skin and nail health. I have seen it personally in many different people. And 3-5 grams of fish oil daily is a must for healthy skin.

Here are my ideas -- Put an area rug over it. -- Find a piece of the carpet, either leftover or inside a closet, and replace that section. I would try this, not knowing whether it would work or not: --Cut a few strands of the rug and take to a craft store and find a matching acrylic paint. You can get a small bottle for a dollar. Water down the paint and then try sponging it into a few strands of the bleached area to see whether it will absorb the color.