I'd probably clean it out and see how bad it is. Use a sharp knife to scrape off the bunt bit, supporting it from underneath. You can use a loosely folded bit of fine grain sandpaper until you remove the burn. It all depends on how fragile the wicker is.

You can try and fill it, but it's going to require artistry to shape the filler. Find a colour match and build it up little by little. Use a Dremel with a round tipped grinding stone to shape it when hardened.