Dumb find-replace-save outlook addin for incoming email. Creating Your First VSTO Add-In for Outlook: https://msdn.microsoft.com/en-us/library/cc668191.aspx

SignatureRemoverAddin.cs

public partial class SignatureRemoverAddIn
    {
        private void SignatureRemoverAddIn_Startup(object sender, EventArgs e)
        {
            var outlookNameSpace = this.Application.GetNamespace("MAPI");
            var inbox = outlookNameSpace.GetDefaultFolder(OlDefaultFolders.olFolderInbox);

            var items = inbox.Items;
            items.ItemAdd += ItemsOnItemAdd;
        }

        private void ItemsOnItemAdd(object item)
        {
            if (item is MailItem mail)
            {
                if (mail.MessageClass == "IPM.Note" && !string.IsNullOrWhiteSpace(mail.HTMLBody))
                {
                    mail.HTMLBody = RemoveSignatureCrap(mail.HTMLBody);
                    mail.Save();
                }
            }
        }

        public static string RemoveSignatureCrap(string body)
        {
            // find and remove stuff here
        }

        private void SignatureRemoverAddIn_Shutdown(object sender, EventArgs e)
        {
            // Note: Outlook no longer raises this event. If you have code that 
            //    must run when Outlook shuts down, see https://go.microsoft.com/fwlink/?LinkId=506785
        }

        #region VSTO generated code

        /// <summary>
        /// Required method for Designer support - do not modify
        /// the contents of this method with the code editor.
        /// </summary>
        private void InternalStartup()
        {
            Startup += SignatureRemoverAddIn_Startup;
            Shutdown += SignatureRemoverAddIn_Shutdown;
        }
        
        #endregion
    }