Looks like you are referring to system log on the server. If that's the case, it is the SFTP/SSH/FTP server (whichever you are using) that's generating the entries. Nothing to do with WinSCP.
I am sending 2000 small files from Window Client to a UNIX host using WinSCP.com. The UNIX admin told me, for my transfer, I wrote 31,000 lines to the system log. (all these messages has my userid on it). How can I supress writing to the system log? I already tried the /log= option.