I don't think the TMDB key would be something entered in a system-wide setting area, I think it would be more likely to be entered in the individual add-ons. Could be wrong, but it would be worth checking Placenta/[insert actual add-on name here
] settings, likely the accounts area. Not got anything with Kodi fired up. Ah, hang on, I'm on a PC....
So Add-on Settings>Accounts>wipe out the existing TMDB key and pop in the one you generated.