Other non-security updates and hotfixes can be safely removed. Service Packs should not be removed as Microsoft no longer supports Office 2013 without Service Pack 1. If there is, you can safely remove it if you take those measurements. If there is no workaround, read the security bulletin for the update to verify whether you are affected by this security flaw and/or if there are other ways to protect you from this. Just a word of caution if the update you are trying to uninstall is an update that fixes a security issue, then it is highly recommended to leave the update installed and see if there is a workaround available for the issue you are experiencing with the update.

Security update, regular update, rollup update, Service Pack or hotfix Note: If you are using a Click-to-Run installation of Office such as Microsoft 365 Home/Personal, Microsoft 365 Apps for Business/Enterprise, Office 2016 Home and Business or Office 2019, see the instructions at Uninstall Outlook Microsoft 365 and Office 2013/2016/2019 Click-To-Run Updates instead. There are several ways to do this depending on the type of update, your version of Outlook and your version of Windows. While in general updates should improve Outlook, on rare occasions updates get pulled due to severe issues or receive a recommendation to uninstall them if you are seriously affected by it. How can I uninstall the update again to verify if the issue will indeed be gone then? After installing an update for Outlook, I'm encountering some strange issues with Outlook which I think are directly related to the update and not to any other Outlook issue.

Microsoft office 2013 uninstall tool