Thanks for the feature request.

What I need from repeat.el
================
When I exit the repeat map---for example when I press <return> in the video,
and leave the "navigation mode" to "edit mode"---I want to unhighight the thing.
That is I propose that there be a provision in `repeat.el` to associate
an `exit-function` with a repeatable map
(put 'thing-sexp-map 'repeat-exit-function 'thing-unhighlight)

The problem with the symbol property name `repeat-exit-function` is that
the existing variable `repeat-exit-function` has another purpose.

For example, for `repeat-exit-timeout` there is the global variable
and the symbol property with the same names because they are doing
the same thing.

But the variable `repeat-exit-function` is different.  It's not
customizable by the user.  So another name would be preferable.

Additional Note
==========
If you squint a bit, `repeat-echo-function` is an `exit-function`
... but the problem is it doesn't provide what map is being exited.
See bug#60353: 30.0.50; Make `repeat-echo-function` as a LIST of functions

Indeed, before adding a new symbol property could you please try to use
the existing `repeat-echo-function`.  It's called with the nil argument
on exit.  Do you need a symbol property `repeat-echo-function`, or can use
the global variable, e.g. by checking some buffer-local variable in it?

I don't need exit function per-map.

I can use the "global" `repeat-echo-function' to clean up after the
`repeat-map`'s exit, like this:

    (add-function
     :after repeat-echo-function
     (defun thing-exit-function (keymap)
       (cond
        (keymap (ignore))
        (t (thing-unhighlight)))))


You have addressed my main concern.  You may close the bug.
    

Some remarks.

1. You may consider introducing a
   `repeat-enter/leave-function`---globally, AND per-map--- and plugin
   the existing `repeat-echo-function` in to that.

   IOW, the "existing" `repeat-echo-function` is a generic enter/leave
   dispatcher for all `repeat-maps`.
   
2. (I believe) introducing an "enter"/"leave" function per-repeat map
   is a much cleaner approach, and could be put to good use by users.

FWIW, the video I linked https://github.com/rnchzn/scratch/issues/1 is
my own take on what `objed` (https://github.com/clemera/objed) does.