There is a reset_bounce_count method in the communication_channels_controller. It's not documented because it's not an API call.
According to the routes.rb, it's
post 'users/:user_id/communication_channels/:id', action: :reset_bounce_count, as: 'reset_bounce_count'
Strangely, the next line mentions a bouncing_channel_report. Calling the route listed makes Canvas say there's nothing there.
The line after that talks about a post that will bulk_reset_bounce_counts.
The communication_channel.rb file has a note to reset bounce count when we're being reactivated.
The communication_channels_controller_spec.rb file says that POST 'reset_bounce_count' "should allow siteadmins to reset the bounce count" but not account admins.
All of that said, I do not know where it is accessible from within Canvas. The closest I can find is as the user themselves, when they go to Account > Settings, they get this:

With some quick playing around, I was not able to get a request to any of internal calls those to work. Mostly getting 422 Unprocessable Entity status codes.
When I go to the Account > Settings > Account Admins, I see that I'm listed as an Account Admin. Maybe none of thise works because I'm not a site admin, just an account admin at the root account level. I don't think I've ever encountered that before.
I share the findings here. It's not a working solution, but perhaps it will spark something that does work.
There is a constant RETIRE_THRESHOLD that is used to determine how many bounces can happen before retiring the account. It is set to 1.