MongoDB document found on replica set but not in mongos
Have you followed this guide from MongoDB to restore a sharded cluster ? Apparently it is different from restoring a non-sharded cluster.

The key here is the backup and restore done on Shards for a sharded collection. The reason for the current state of your database is because, config server or cached information on Mongos are not aware of the restoring happened on Shards. So the meta information stored on config servers doesn't have latest information about the distribution of the data in shards.

You can try getting into proper state, 


By restoring the cluster by following the guide.
by tying to remove shard and re-adding the shard again. So that MongoDB would drain all the the data from one replica-set to the primary replica set and then re-balance the data, after re-adding the shard. You may use, removeShard and addShard operations.