How do I fix/repair wood look laminate?

Have your thought about buying a counter top kit to refinish. This will give you an updated look and really is not that hard to apply as long as you follow the instructions. Everything you require is usually included in the kit. The kits come on sale periodically so watch for a good sale.

That looks like a Stain from a pot that laid on there too long.

You can try an SOS Pad, with scouring powder like Comet, or even give it a Soak in Vinegar, but that can damage the sheen. So it really relies on how fussy you are.

No Cleanser will really fully resolve that. It is absorbed in.

For a Higher degree of Satisfaction, You need to Power Sand the Entire and apply a coat or two of Polyurethane after you evenly sand the stain out.

It is unfortunate but if you are fussy as I am: You can try & try and get a degree of satisfaction but you by knowing where it was will yet see the spots and residues.

If it is in a good spot, you could always put a cutting board over the area until you can get it fixed up to hide it, or leave it in place all the time. I have an area next to my stove that I keep a cutting board out all the time as other inhabitants of the house was using the laminate as a cutting board and I was afraid it would get damaged since it is right by the knife blocks.

You can always cut it out and replace with tile for a permanent hot plate.