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Is it a built-in preset or a user preset?
The built in presets are part of the program and can't be deleted.
On the right side under metadata there is the preset button. When I enter the metadata for shoot/project the metadata I can't delete.
I understand you are looking for the Metadata presets to apply at Import- (and delete some)
In Lr, Open the Preferences dialog (Ctrl+,), select the Presets Tab, click on the button [Show Lightroom Presets Folder]
Expand the 'Lightroom' Folder, then expand the 'Metadata' folder.
The default location for the Metadata folder in a PC will be like:
C:\Users\Your Name\AppData\Roaming\Adobe\Lightroom\Metadata Presets
Delete the presets from this folder.