We have the latest backup of distribution database. But the data on publisher changes every minute
If you cannot restore the distribution db, you will have to reintialise from snapshot. You're publisher transaction logs will continue to grow until you recover the distributor as the log cannot be cleared until all replicated commands are committed there. This is good, as it means once recovered, the log reader will know everything that still needs to replicate.
So first we have to clear the publications not to use distributor and remove the publisher from replication.
If you do this, the above doesn't apply. As soon as replication is removed, the next transaction log backup will go through and clear out all of the commands. You will need to reinitialise the subscriber in some way.