You could run a server-side process to purge documents older than 7 days, if you don’t want to keep them on the server.
If you want them on the server but just don’t want your client to pull them, it’s a little tricky since you can’t assign docs to channels by relative dates (a doc only gets assigned to channels when it's updated, when its age is by definition zero.) The advice I give is to define per-week channel names (like “2015-01” for the first week in 2015) and have the sync function assign a doc to one such channel based on a timestamp property in it. The client then comes up with the channel name for the current week and explicitly pulls that channel.
—Jens