In a event when the previous page contents are remembered, then in the event, one of the evicted pages is needed again before it has been overwritten. It can be reclaimed just by deleting/removing it from the pool of free page frames.
For your information, keeping the supply of page frames around yields much better performance than using all of the memory and then trying to find a frame at the moment it is needed.
The paging daemon (a background process to insure a plentiful supply of free page frames) insures that all the free frames are clean, they needn't to be written to disk in hurry whenever they are required.
A two-handed clock is a way to implement this cleaning policy.
In this two-handed clock, the front hand is controlled by paging daemon. Whenever it points to a dirty page, then that page is written back to the disk and front hand advanced. And whenever it points to clean page, then it is just advanced.
And the back hand is simply used for page replacement as in the standard clock algorithm. Now, the probability of the back hand hitting a clean page is increased just due to work of paging daemon.