Is this the only mark on the coaster? It is rather badly worn, so please post a photo of any marks on the second coaster.
This type of coaster is usually used with teacups. Traditionally, a Japanese teacup has no handle and when filled with hot tea, it can be very difficult to pick up. The long ends of the coaster serve as an edge by which the cup can be lifted to the mouth without directly touching it.
These coasters are very common in wood or pewter, less common in copper, and uncommon in silver. The mark shown is that of the retailer, so if there is no other mark the coasters may not be silver. They may also be unmarked silver if they were part of a larger set in which principal pieces were marked. If the coasters are pewter, they were probably part of a sake set, in which case the divets will be smaller, as sake cups are smaller than teacups.