Hello, not sure what is the component and view in your picture.
I made a test in business role SALESPRO, searc a service order. The item for it is BT115IT_SLSO/ITES.
It is in method CL_BT115IT__ITEMS_CN00->GET_OCA_T_TABLE to render the delete and edit buttons. I don't see authorization check for these two buttons.
Maybe you should find out the method where the buttons are rendered for your component and view, and then add your own logics there to control the display of them.
Best Regards, Corrine