Hi Trish,
To achieve your goal, we can edit the SQL Server Reporting Services Report Viewer Web Part's tool pane. Please refer to the following steps:
1. Insert a SQ Server Reporting Services Report Viewer Web Part, click "Click here to open the tool pane" inside the SSRS Report Viewer web part.
2. Click "OK" in the pop-up dialog box.
3. In the tool pane, expand the "View" item, then you can customize the Report Viewer ToolBar Items visibility freely.
The screenshot below is for your reference:

Regards,
Mike Yin
TechNet Community Support
