To remove the buttons/links simply configure them as display type "linkbutton" and specify the text as an empty string.

[xmod:editbutton display="linkbutton" text=""/]

[xmod:copybutton display="linkbutton" text=""/]

[xmod:deletebutton display="linkbutton" text=""/]

 Replace "[ ]" with "< >"

From the fatgeorge fileupload user guide

Delete Image Button

If you are using UploadandSelect method once you have uploaded an image the file browse and upload control should disappear and the image will be displayed (DNN 3.3.1+/4.3.1+) along with a delete button.
Clicking the delete button will delete the uploaded image along with any generated files such as thumbnails.
The file browse and upload controls will become visible again.

Deletelinktext

The text of the link the user clicks to delete the file they've uploaded. The default value is 'Delete'. (Optional)

** PLEASE TEST FIRST ON TEST DATA **