There are two things you need to think about when updating terms. First is the actual term on the list item, and the second is optional if you have managed metadata refiners, and that is to update the term in the index (the old value will show up in your refiners even if you fix the first issue).
To Update Terms on list, here's a PowerShell script you can use (leverages PnP-Powershell), but the most important item is the last line where you call UpdateUsedTermsOnSite...
$tax = Get-PnPTaxonomySession
Get-PnPProperty -ClientObject $tax -Property "TermStores"
$ts = $tax.TermStores
$site = Get-PnPSite
To update the index so the content, you may need to force a reindex of the content if no other changes were made.
Hope that helps!