fretka2: Well, I figured out how remove the text (without cheats) on my own.
To make the annoying text go away (with cheats off), I restarted the game with the command line "+set developer 0 +set thereisnomonkey 0 +set cheats 0". This turns off cheats, but it also turns off that annoying text that kept appearing after previously using cheats.
I didn't enable "+set ui_console 1" when I was using cheats, so if anyone did then you may also need to reset this value to '0' on your next restart.
I'm still curious if there's a way to run the game with cheats on, but without the annoying "Axis NPC Allies NPC" text on screen. If anyone knows, please share.
A little late, but you can do it if you restart the game with the proper command lines (" +set cheats 1 +set ui_console 1 +set thereisnomonkey 1") while console is disabled in the options menu (options/advanced/uncheck the box next to "console") and start a new mission as it doesn't work on saved games. If the text still appears add "+set developer 0" and restart again.