you can find this input field in manager/frames/menu.php on line 226, maybe give it a hidden type?
ex: <input type="hidden" ...>
Thank you, breezer.
In the meantime I realized that the issue does not occur on a local installation of MODX 1.0.8. But there I saw that in the configuration I have just the standard theme "MODxCarbon".
In the live site I had switched to the theme "MODxLight" (as you can see in the screen shot), but it's now obvious that this was a leftover from the old version. Switched back to MODxCarbon and the issue was gone.
Conclusion: The bug is in the MODxLight theme.