The solution I explained above is NOT something you want to use in a production environment on a regular basis. It must be considered as a last resort action when nothing else is suitable (for example a full restore of a daily backup).
You can’t trust this solution to work each time because the oplog is a capped collection and old documents will disappear from it eventually.
For sharded clusters, you’ll have to apply the same method “locally” on each shard because mongos can’t access the system local database. Each shard has its own oplog completely independent from the other shards.
Again, to me, this is an extreme mesure that should never be used. When you remove a document in MongoDB, you should consider that it’s gone for good. If recovering old docs is part of your requirements, I would use another strategy like “soft deletes” (i.e. just set a boolean {deleted:true} and use it to filter with an index).
Cheers,
Maxime.