Truth is, the patch will always show. Even if this is a flip, it will not look right. For all the time and trouble, you may as well rip out the entire piece of MDF and replace it.
This does not look like it is on the hinge side, so it is a simple pry and replace. If the hinge side is exploded too (MDF and water do not get along) then rip out the entire frame. For a weekend warrior, it might even be better to rip out the entire door, get a pre-hung replacement, and put it in ... The time spent trying to patch might produce an inferior outcome.