Skip part of script on error

I've been banging my head against the wall for awhile on this one. No amount of Googling has yielded me any successful results thus far. Wondering if someone can give me a hand?

# Load the PowerShell module for Active Directory
Import-Module ActiveDirectory

# For each computer in AD that is a member of the target group
Get-ADGroupMember -Identity "CN=RenameComputer,CN=Users,DC=int,DC=example,DC=com" | ForEach {

        # Define the new name as the old one, minus one letter at the end
        $NewComputerName = $_.Name -replace ".$"

        # Perform the rename operation
        Rename-Computer -ComputerName $_.Name -NewName $NewComputerName -Force -PassThru -Restart -WhatIf

        # Remove the computer from the target group
        # THIS SHOULD NOT OCCUR IF THE RENAME ABOVE FAILED!!!
        Remove-ADGroupMember -Identity "CN=RenameComputer,CN=Users,DC=int,DC=example,DC=com" -Members $NewComputerName -WhatIf

}

TL;DR: This script finds a bunch of computers in a designated group, renames them, and then removes them from the group. I need help telling the script to NOT remove them from the group in the event that the rename fails (machine is offline, etc.) or throws some error.

Thoughts?

Thanks in advance!