You can select an existing preset in the Watermark editor, then the same menu includes an option to delete that. Wherever presets can be saved in LR, there is generally (maybe always?) also a way to delete these, provided in the same place. Also (though exceptionally, not for Watermarks) there is usually a way to update a saved preset using current settings.
More generally, presets are just text files (".lrtemplate" file type) and the LR Preferences / presets tab includes a button which opens the location on disk where all the various presets subfolders live. Items within can simply be deleted from there... and also backed up, inspected or altered with a text editor, copied across to another computer, and so on.
Also (though exceptionally, not for Watermarks) there is usually a way to update a saved preset using current settings.
You can for watermarks too, but like other presets that use a single pop-up, you have to select that particular preset, edit it so that the name changes to (edited), and then it'll let you update it.
Thanks, that makes both more sense in specific terms, and also less sense (in overall interface terms).
Looking at the posted screenshot menu, the option has now been withdrawn to delete the preset, if we wished to do so (which prompted the original query). So the steps we would now take to retrieve that menu option... are not apparent. Maybe we'd have to update the preset first before we could then delete it... which is IMO slightly odd logic.
Hmmm. Was it necessary for this menu to be so elaborately parsimonious?
I have a problem related to this...
I acidentally removed the files used for my watermarks, and now I cannot select the watermarks from the menu to delete them... I try to select the watermark from the dropdown menu, and any of the ones with missing files just close the dialogue box when I select them. When I reopen the box nothing is selected, and this occurs ad infinitum... I really just want to start fresh with new marks.. If I could delete them all it would be better than having all these useless marks..
wako-jako: to delete watermarks, you can go to the location of your presets as shown here - http://helpx.adobe.com/lightroom/kb/preference-file-locations-lightroom-4.html
There are various folders there for Develop presets, import presets, etc. One of these is "Watermarks" - your user-created watermarks are stored inside as structured-text files with the extension ".lrtemplate".
Just delete, using your operating system's file browser, whatever you don't want.
Or, if you prefer, you may be able to re-address the watermark onto some kind of graphic by editing the "imagePath = "xxxxx",