Hey Jason,
Unfortunately Keyboard Maestro doesn’t provide an automated method of closing these windows. It’s fire-and-forget…
Nevertheless there is a means to do it using AppleScript and System Events:
tell application "System Events"
tell application process "Keyboard Maestro Engine"
tell (first window whose name contains "clipboard")
tell button 1
perform action "AXPress"
end tell
end tell
end tell
end tell
-Chris