Delete resource is actually delete it from the database, the resource in other collections will also be deleted.
So I guess the collection you selected is not enough, you may try to add the "All Systems" collection to the security scope to see if it work.
Permissions to delete a resource in a collection
Hello,
When trying to delete a resource from a collection I am getting an error:
Which permission(s) did I miss?

Any permission(s) outside the collection bucket?
Thanks,
Dom
Microsoft Security | Intune | Configuration Manager | Other
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AllenLiu-MSFT 49,436 Reputation points Microsoft External Staff2022-02-23T09:49:37.78+00:00
4 additional answers
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AllenLiu-MSFT 49,436 Reputation points Microsoft External Staff2022-02-23T08:28:44.887+00:00 Thank you for posting in Microsoft Q&A forum.
I did a quick test in my lab environment, I just add the "Delete Resource" permission of Collection for the security role "Read-Only Analyst".
And it's enough to delete a resource in collection.
You may check the Security Scopes for your user to see if it has enough security scope?
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AllenLiu-MSFT 49,436 Reputation points Microsoft External Staff2022-02-23T08:45:41.517+00:00 I'm confused. Why do you create permission for each collection? And how?
What I did is create a custom security role and assign it to a user:
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Duchemin, Dominique 2,011 Reputation points
2022-02-23T08:35:12.547+00:00 Hello,
I had already these permissions on Cllection #1 but it did not work...
So I added the same permissions on the "Limiting collection" #2 as well..
Thanks,
Dom -
Duchemin, Dominique 2,011 Reputation points
2022-02-23T09:01:29.297+00:00 Correct for the security role
but I added the "limiting collection" in the Administrative user.

Thanks,
Dom