To remove an attachment you should edit the layer. If you are the designer of the WAB application you should add the hosted feature layer with edit capabilities and use the Edit widget—Web AppBuilder for ArcGIS | ArcGIS to delete the related record.
Just go into your web map and configure the pop-up. Below the list of field there will be an option which allows you to switch the hyperlink to the attachment off (see below, sorry for the Spanish interface):
As far as I can tell you are using the GP widget, or is it a different one? Where does the result point at and what does it consist of? Is that the same layer that already exists in the web map? In the GP widget configuration of the results tab, do you have the possibility to switch it off there?