It depends on how deep the burn is and what material the worktop is.
Looking at the image it's not too badly burned. A good test is to wet the burned area with water. If the mark disappears then it's likely easily repairable, otherwise it might require a more substantial approach.
Not 100% clear from the image, but it seems to be a basic kitchen worktop - laminated/veneered chipboard/particleboard.
If this is the case, then you can try some of the following ideas:
Clean the surface with a clean damp cloth (water only) to remove dust/debris. Any debris there can score the area badly when using the following methods to fix the burn mark.
This stage can show you whether the stain disappears when wet.
Buff/Polish with Cleaner approach
Abrasive cleaners or other substances such as toothpaste and bicarbonate of soda can "re-polish" the surface if it's only lightly marked.
This would likely require some lacquer to have remained underneath the burn to be able to polish it up. The water test can be a good indication of whether it can be polished up or not (though not all circumstances are equal so evaluation and slow test is key here).
Don't use too strong an abrasive cleaner, use a soft damp cloth, and press gently.
- You are trying to polish the lacquer/glaze, not scrub away the burn
Apply a very small amount of the substance (such as Cif (or similar), or toothpaste and bicarb together) to only a small part of the burned area. Very gently rub the marked area with a soft damp cloth. Rinse off with clean water, pat dry, and wait for it to fully dry (20 mins ish) and see what it looks like.
Analyse the results, and if you are happy it's an improvement, repeat across the rest of the marked area.
Don't suddenly get excited though, keep it simple and only apply a little substance and soft cloth, and only do it for a short time. Rinse with clean water and leave to dry again.
Just because one small area has come back up doesn't mean it all will, so keep "test" and "small progress" in mind.
This won't likely be done and dusted in 10 mins, and if you want the problem to be resolved, put aside some hours.
Good thing is you don't need to stay with it. After rinse, go and do whatever else for 20 mins or more, then come back, even the next day if needed.
Don't go too far!
- If positive results are happening keep it slow and simple, wiping
clean and leaving to fully dry for further inspection, until the
stain is removed. While you are polishing up the lacquer under the
burn mark, going too far means you risk removing any renaming
lacquer, then there is nothing to "polish"
Iron and tea towel
This method usually works better with varnished or other types of finished surfaces, but it may work.
You do need to take this one slowly as this can also make the problem worse or increase the size of the burn mark.
Take a clean, dry tea towel and place it over the burn mark.
Get an electric clothes iron, and with steam setting OFF, gently press on the tea towel where the burn mark is. Don't leave the iron on, gently press down for a second and then back up. Do this a few times and remove the tea towel and check for results.
If there's no additional damage, or nothing has changed, or improvements are being made, repeat again slowly and for only a short time.
How long you do this for etc depends on how deep the stain is, and what material the surface is.
If after doing this for a while you feel there are no results, you can try turning the steam setting ON. However, be careful here as this can also cause burn damage!
This method really does need a very slow approach and only apply the iron with steam very briefly and check the surface for results.
WARNING: The above advice is only advice, and care is to be taken to evaluate the intensity of the damage and the work surface before trying the above methods.
Using the wrong method or substance may very easily make the burn mark worse!
Even some laminates can have varying lacquer thickness. So there's no one rule fits all, you just have to be careful and go slowly.
Never place a hot iron directly on or above the work surface (without tea towel etc). It will possibly cause damage.
You are not likely to make the overall problem worse given there is already damage, but you can increase the size or intensity of the damage if you go to hard with one of the methods, and then another method which may have worked, might no longer due to increased damages.
Just go steady :)
You can buy repair kits, which usually consist of paint and lacquer, but they're not cheap and often not cheaper than fitting a new worktop.
Cost comparison depends on the worktop (is it a cheapy one etc) and how much of the worksurface you need to replace (i.e. is it a small piece near a join etc).
Painting worksurfaces is also usually done when you want to change the entire colour. However, if done correctly, you can get some amazing results.
Obviously if you are avoiding costs for repairs you won't want to do something like this, but it is a viable option with amazing results.