Is it possible to hide or remove the 'delete' option once someone has submitted a list item? I've Googled but haven't found the answer.
You can create a Permission Level that does not allow deletes.
Click Site Settings->Site Permissions->Permission Levels
Click Add a Permission Level and give it a name like “Add - Edit - View Only”.
Check “Add Items”, “Edit Items”, “View Items”, “Open Items”, “View Versions”, “View Application Pages”, and “Create Alerts” under List Permissions.
Check “View Pages” and “Open” under Site Permissions.
Check “Manage Personal Views” under Personal Permissions (if you want).
Then edit the Permissions on the list and assign this Permission Level to your users and the Delete buttons will not appear.
check out the below link , it will show you how to hide the ribbon's delete button in Sharepoint 2013
SharePoint 2013: Hide/Show Delete Icon In Ribbon On List Item Selection