The Select attachments button is built into an attachments-type tab and cannot be hidden on its own. To remove the button, you must delete the attachments tab. Attachments may still be collected elsewhere in the form through the use of file upload (single) fields.
Delete the attachments tab
In the Manage workspace, go to Applications
Click Edit form and choose a form
Click the settings icon next to the attachments-type tab
In the configuration tray, select Delete
Restore the attachments tab
If you need the tab again, you can restore it at any time.
In the Manage workspace, go to Settings > Applications > Tabs
Open the All but deleted toggle
Select Deleted
Click the checkbox next to the tab
Click Undelete
Switch the view back to All but deleted
Good to know
Any fields on the tab should be moved before deletion using the form editor.
Deleting a tab does not delete fields permanently.