How do I fix burn on outdoor rug?

I found a tutorial for you. I hope this helps, Amy: https://www.hometalk.com/diy/floors-ceilings/out-out-burn-mark-on-my-carpet-34203395

I would scrape off as much of the brown burn mark as I could with a plastic spatula or credit card and then buy some small bottles of acrylic paint and touch it up. You might even try a light sanding with fine grit sandpaper--carefully--so you are just sanding the burn mark and are only removing the discolored area--not all of the rug fibers. It looks like a very small mark so this may help you disguise it.

Try and scrape out fabric of carpet from underneath and use superglue to glue in what u scrape out

I’m pretty sure you can’t restore the texture, but magic markers in the colors of the rug could mask the burn.

Hello, I would consider touching it up with acrylic paints. The type you see at Walmart or the craft store for about $.50 per color. I would suggest the flat sheen over the satin or gloss.

The link to the post above shows using hydrogen peroxide. Be very cautious with this as it can bleach out the carpet.

Yup. You can't "fix" it but you can disguise it. Scrub up all the scorched marks and use a permanent marker or acrylic paint to recolor the area. Looks like you'll need 4 colors to replace the pattern: teal, ecru, tan and light blue. Take this pic with you to the store to match the colors as best you can. For paints, if in doubt, go with a lighter color or mix in some ecru or white to soften the color. I'd use a stencil brush to dab it on. Keep the paints and brush handy in case it wears off over time.

The first answer with the link provides a very good starting place. You need to remove as much burnt color from the fibers as possible. The rug in the link is an off-white, which is why the hydrogen peroxide works very well to finish lightening the burn mark. Hydrogen peroxide should also work on your rug, especially the off-white, while not removing color from the pattern.

Nonetheless, the colors may be more difficult to fix. Permanent marker colors are limited, so it's unlikely you will find a match. I would buy near matches of acrylic craft paint in 2 oz bottles for the teal and pale blue areas, if needed. Adjust a too dark color by adding some white. Any acrylic paint should be permanent once dry and cured.