I know we can use CSS on Classic Forms. But not having this is a problem for the responsive forms.
I believe this has to be adjusted through SharePoint by creating a custom permission group. In the custom permission level, you need to uncheck the box that says, "Delete Items" under List permissions. Then it should go away. Since you can't add custom CSS in the responsive forms, I don't think there is another way.
Thank you for the suggestion, but we really don't want to have that kind of granular permissions. Hiding is generally enough.
If a complicated workflow assigns tasks to multiple users and one 'idiot' deletes their task, I would have to get everyone else to abandon their already completed tasks and start again.
It makes perfect sense to have this kind of 'hide delete button' as an option, if our CSS is blocked. There are CSS settings in Responsive forms. But very limited so far. Adding ribbon options here would be helpful.
I have added this to the Uservoice page as a suggestion.