Tudor Rain Gutters

[Richard in Anaheim CA]

My rain gutters have popped out for about 2 feet behind the windshield.
The tack holes are black and rotted. I'm thinking to remove the rain gutters and plug those holes with a hardwood plug in each nail hole.

How do I remove the rain gutter from it's channel to get down to the wood? Tap it forward from the back with a wood block? Any other suggestions besides all new wood?

Richard
ANAHEIM CA