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Are your test cases just standard issue types of Jira or are they provided by any third-party apps? Can you please provide us with more context about the feature you are talking about?
If they are standard issue types, you must have the delete issue permission in the related project to be able to properly delete them under project settings > Permissions. These would be the steps to check if you have the permission and properly delete it:
- Navigate to the project related to the test cases > Project settings > Permissions
- Check if your user is added to any of the groups/roles added with the delete issue permission, optionally using the permission helper at the top-right corner of the page
- Once you confirmed that you have that permission, navigate to the test case you want to delete > Click at the three dots icon (...) at the top right corner > Delete:
Let us know if you have any questions.
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