Hello,
If the user has permissions to edit the post, they would be able to see the edit buttons. You cannot disable this.
If you need to remove it, you can modify the theme file to remove it if you want:
Modify and create overrides for the following files:
Listing:
/components/com_easyblog/themes/wireframe/listing/card.php
/components/com_easyblog/themes/wireframe/listing/default.php
/components/com_easyblog/themes/wireframe/listing/nickel.php
/components/com_easyblog/themes/wireframe/listing/simple.php
Entry:
/components/com_easyblog/themes/wireframe/entry/default/default.php