Location removal for cloud storage is disabled if there are archives on that storage. The only way to remove the vault via API, you can use RESTer browser plugin or other tools (e.g. Postman) to send a direct DELETE request to the vault manager.
To find the ID required for the delete request, select the backup location -> Details -> All properties -> scroll to find id parameter, with the following format: xxxxxxxx-yyyy-zzzz-yyyy-xxxxxxxx. Alternatively, scroll to the very bottom of the list and find vault_id.
Log in, make sure to select a machine to browse from to the one showing wrong archive information, and then using RESTer plugin for the browser, send the following request:
Method: DELETE
URL: https://<DC>-cloud.acronis.com/bc/api/vault_manager/v1/vaults/<id>?action=unregister
BODY: {"action": "unregister"}
Headers: <Copy cookies from any authorized request to <yourDC>-cloud.acronis.com>
where <id> should be replaced by either id or vault_id.
How to find proper cookies:
1. Log in to the affected customer's account. In the browser, open Developer tools -> Network (usually, developer tools can be opened by pressing F12):

2. Click on any link related to an activity and select any of the requests:

3. Go to Headers:

4. Go to Request Headers and select Cookies:


Copy the contents of the Cookies. Go to the RESTer plugin interface, move to the Headers tab, and paste the cookies and set Content-Type as application/json:

In the Body tab, switch the format (menu with three vertical dots) to JSON:

The resulting request will look similar to:

Expected request response is 204 No content.
This request removes the vault from vault manager and in Activity tab you should see "Removing vault from agent" activity.
To add the cloud storage backup location to the list again, run a backup to that cloud storage. It will be added to the Backup locations list automatically.