Salicylic acid is a beta hydroxy acid and is extremely well known in treating acne. While most people use it to treat acne, salicylic acid has actually been used to treat other skin disorders, that too for more than 2,000 years. The reason it is considered very effective is due to the properties that it has that makes it a good peeling agent.
Peeling is generally considered as safe and effective method to rejuvenate the skin, smooth it out, and improve the surface texture. Salicylic acid as a peeling agent has the ability to dissolve crusty skin, which is why it can be helpful in removing seborrheic keratosis.
If you're going to use salicylic acid to treat seborrheic keratosis, it is best to get the right concentration prescribed by your doctor that would actually give you results. Sure there are over the counter options too, but the concentration may not be high enough.