Thank you for your post.
I am unable to replicate the problem. I have several privilege sets that allow me to add/edit records, but do not delete. I've opened these files under FileMaker Go (on iPad, iPhone and iPod touch), and the privileges will not allow me to delete a record.
Try using the built-in Guest account and see if you are able to delete records.
Perhaps you can provide more information/details about the privilege set being used.