Since you are keeping a copy for everyday, I'm assuming the "XXXX" in your backup file name is MMDD, or something like that. If so, just determine which day(s) you want to delete, create a string representing the MMDD, build a string that does a delete on that file including the full path name, and use xp_cmdshell to make it disappear.
If that's not it, we need more info, as I know you don't have multiple files in the same folder all with the same name.