Here is the working solution I ultimately wound up using. It is based on tarsius' advice, who deserves all the credit.
(defun kill-magit-diff-buffer-in-current-repo (&rest _)
"Delete the magit-diff buffer related to the current repo"
(let ((magit-diff-buffer-in-current-repo
(magit-mode-get-buffer 'magit-diff-mode)))
(kill-buffer magit-diff-buffer-in-current-repo)))
;;
;; When 'C-c C-c' is pressed in the magit commit message buffer,
;; delete the magit-diff buffer related to the current repo.
;;
(add-hook 'git-commit-setup-hook
(lambda ()
(add-hook 'with-editor-post-finish-hook
#'kill-magit-diff-buffer-in-current-repo
nil t))) ; the t is important