To this date there’s no function to delete a plug-in effect preset in Ardour. A feature request has been filed and you can follow the status here. In this case we will delete an obsolete duplicate that has been saved under the same name.

Open the file:
~/.ladspa/rdf/ardour-presets.n3
On my system the .ladspa dir is located in the user home dir. If you’re using a file browser make sure you enable the “show hidden files” function. Before you edit the file remember to keep a back up.

In the image below the highlighted part represents the duplicate preset.

When the highlighted part is removed the preset is also removed. Open Ardour and have a look.

This works for every preset and to find the desired preset to be removed, start by searching for the name of the preset (line including #hasLabel). Then select everything from two lines down (line including #hasSetting)  up to the line below including next“#hasSetting” and delete selection.