Hello,
As we understand, you need all the unwanted characters to just be removed from the generated emails before checking them for uniqueness and setting for a user. To achieve the desired, use the below script. In the script, we added the $excludeCharacters variable that specifies the characters.
$initialEmailTemplate = "%firstname:lower%%lastname:lower%@mydomain.com" # TODO: modify me
$secondaryEmailTemplate = "%firstname:lower%%initials:lower%%lastname:lower%@mydomain.com" # TODO: modify me
$excludeCharacters = @("-", "'") # TODO: modify me
function CheckEmailUniqueness ($mail)
{
    # Build search criteria
    $criteria = New-AdmCriteria "user" {mail -eq $mail}
    # Search for users with the username or email address specified
    $searcher = $Context.TargetObject
    $searcher.Criteria = $criteria
    $searcher.VirtualRoot = $True
    $searcher.SizeLimit = 1
    try
    {
        $searchResultIterator = $searcher.ExecuteSearch()
        $searchResults = $searchResultIterator.FetchAll()
        return $searchResults.Length -eq 0
    }
    finally
    {
        # Release resources
        $searchResultIterator.Dispose()
    }
}
function UpdateUser ($mail)
{
    # Update the user
    $Context.TargetObject.Put("mail", $mail)
    $Context.TargetObject.SetInfo()
}
# Check first template for uniqueness
foreach ($character in $excludeCharacters)
{
    $initialEmailTemplate = $initialEmailTemplate.Replace($character, "")
}
if (CheckEmailUniqueness $initialEmailTemplate)
{
    UpdateUser $initialEmailTemplate
    $Context.LogMessage("$initialEmailTemplate set as user email.", "Information")
    return
}
# Check second template for uniqueness
foreach ($character in $excludeCharacters)
{
    $secondaryEmailTemplate = $secondaryEmailTemplate.Replace($character, "")
}
if (CheckEmailUniqueness $secondaryEmailTemplate)
{
    UpdateUser $secondaryEmailTemplate
    $Context.LogMessage("$secondaryEmailTemplate set as user email.", "Information")
    return
}
$Context.LogMessage("Could not generate a unique email address for user %fullname%.", "Error")