We have a match!

AllRowsExcludingStupid.ps1

$DatabaseParam = @{
    SqlInstance = 'localhost\SQLDEV2K14'
    Database = 'DMODisabled'
}    
Get-DbaDatabase @DatabaseParam |
    Select-Object -ExpandProperty Tables |
    Where-Object { $_.Name -notmatch "\d{4,6}$" } |
    ForEach-Object -Process {
        [PSCustomObject]@{
            Name = $_.Name
            RowCount = $_.RowCount
        }
}