I suggest using aStanley knifeto cut around the damaged area. Once you've removed the damaged pieces, wash the area with soap and water to remove all the oil and grease on the laminate surface. It's important the surface of the laminate be free of dirt and debris so that when you glue the vinyl patch it will not slide away.
Using your Stanley knife cut a white rectangular piece that is larger than the damaged area. Please note that the vinyl will not be the same colour as your laminate surface. The purpose of putting the patch on is to prevent food and grease from entering the damaged area. Once the area is totally dry apply some of the contact adhesive. Although the vinyl panel already has adhesive on it the contact adhesive will provide a superior seal over the area. Please make sure to follow the instructions on how to apply the contact adhesive.
Another way to disguise the damage is to cover the front area of the stove with a white vinyl panel. In this manner, it will look like it is a protective covering for that area of the benchtop. - EricL