Is there a PowerShell “string does not contain” cmdlet or syntax?

If $arrayofStringsNotInterestedIn is an [array] you should use -notcontains:

Get-Content $FileName | foreach-object { `
   if ($arrayofStringsNotInterestedIn -notcontains $_) { $) }

or better (IMO)

Get-Content $FileName | where { $arrayofStringsNotInterestedIn -notcontains $_}