How to ship new rows from the source to a target server?
It sounds like in this case, a simpler solution might be best for you, such as scheduling a daily SQL Agent job that INSERTS INTO the Target Database's Table the 10 million rows you need from your Source Table. If you're always deleting those 10 million rows from the Source Table after they get sent to the Target Table then it sounds like a pretty simple INSERT statement.
You'd have to remotely INSERT INTO the Target Table which can be accomplished via a number of means such as with a Linked Server and/or OPENQUERY.
Part of your SQL Job will need to manage exceptions for if the Target Server is offline, based on your own retry / abort logic.