Change your job to protect partial organisation, and select sites, this way it will do every site. You can optionally then add an exclusion for personal sites

To do so, add the organisation to a backup job then edit the processing type to just sites:

https://helpcenter.veeam.com/docs/vbo365/guide/back_up_organization.html?ver=80

So I do have a job that is just backing up sites, not the entire org. Object checked are most of the sites including the deleted one which is not a personal site. It is a department test site created by my manager. 

I am asking if there is a way for tonight’s backup job to not include it since it’s deleted and giving warnings it can’t be found during backup, without me removing it manually from included objects, or adding it to excluded objects. I just want it to disappear from the next job when it is deleted by the user.

It seems this test site got added to the backup automatically upon creation since I didn’t add it to the job, but can’t be removed automatically. 

Hi,

Based on what you’re saying, you’ve ticked specific sites, not selected the organisation and editing what is processed to sites. Is that right?

Yes the job is: Backup following objects (instead of entire org)

Select objects: uncheck org and checked 21 of 23 sites. (deleted site ‘Test1’ is checked here)

Exclude object: none

So to resolve I would go to ‘select objects to back up’ and highlight Test1 and remove it. But I want it to remove on it’s own since it can no longer be found during job. If that is possible.

This is where I’ve been trying to advise you, so you’re correct to not have the “entire organisation” option ticked. When you choose what objects to add, you can specify users, groups, sites etc, but you’ll also have an organisation option. Choose this, select your organisation. You’ll see it appear in the list. Once you’ve done that, select the object from the list and choose the edit button, untick the options other than sites. Your job will now be automatically catching all SharePoint sites that exist in your tenant, enumerated at every job run

Ahh I understand now! I kept selecting Sites from the dropdown and didn’t see Org listed there as well! My job object is now only my org instead of the list of sites, and I edited it to only backup sites. So now I assume my org sites that exist will be backed up now instead of managing individual ones in the list of objects. I will test this out tonight, thank you!!