A great option is to use linoleum shavings of the same shade/texture and mix it with wood glue to get a paste and apply it on the scratches. Level it out wel and allow it to dry- bingo! Your scratch has disappeared!
The best and professional way of repairing scratches is to cut out the bit and use a new bit of linoleum of the same texture and design to fil the gap. It's more strenuous and can be a little more expensive. Otherwise try out some inoleum repair kits thatare available.
To fix linoleum scratches, mix some wood glue with shavings from similar linoleum material and apply this paste evenly. Keeping few pieces of extra linoleum material after installation comes handy for this purpose.
If you have some extra pieces of linoleum, take those pieces and make shavings. Mix these shaving with wood glue and then apply the paste evenly onto the scratches. You can also purchase linoleum repair kits.