Hello,
you can delete all attachments matching the "filename" like this:
MailMessage mail = new MailMessage();
mail.Load(@"C:\temp\mail.eml");
for (int i = 0; i < mail.Attachments.Count; i++)
{
Attachment item = mail.Attachments[i];
if (item.FileName == "filename")
{
mail.Attachments.RemoveAt(i);
i--;
}
}