Tasting Sap gone Bud

[MichtonTree]

I pulled my taps last week. My first year Sugaring. My wife back from taking our dog for a walk on our property, as she does each morning, came up to me today and said the sugar maples are still weeping. "Are you missing out on sap". Temps have been in the 50's and 60's. So I went over to take a look. One of the trees I looked at there was a puddle on the floor from so much sap flowing, the rest were dripping as well. When I stuck my finger in to stop the flow and removed my finger it would literally gush out. I tasted the sap...I now know what buddy sap taste like, it was awful.
Question: How long before the trees heal it self?
My wife felt bad for the trees as if they were bleeding, which I imagine it is.
I know not to plug the trees or put anything in the hole, but was wondering, does it stop once the buds have opened?
Any info is appreciated. Thanks.

[Run Forest Run!]

They'll stop weeping really soon. It doesn't take long at all and you'll be able to look at the trees again without feeling guilty.