SQL server: create local copy of remote table
You may want to consider transactional replication, which would allow you to have an initial snapshot of the table copied from the source system to the target system. After this initial snapshot, you can then configure transactional replication to push the data changes to the target system.

The requirement for transactional replication is that the table has a primary key, however, it is a feature that I have used for the purpose you described on many occasions. 

Bear in mind that replication would need to be activated on the source system and requires some administration to ensure it runs correctly. However, for a single table syncronization setup as described, it should cover everything you need.