In the habit of Gnome applications, Cheese stores its configuration data in the dconf configuration system rather than in plain files.
To access that, you could use a GUI program called dconf-editor from the package dconf-tools  :
:
sudo apt-get install dconf-tools
Cheese uses the /apps/cheese/org/gnome/cheese(since 14.04) gconf path:

You could easily play with the settings (they all typically have well-documented schemata displayed in the bottom of the dconf-editor window), and, ultimately, wipe the  settings clean by resetting the values to defaults (non-defaults are highlighted with bold font as you can see on my screenshot).
Besides dconf-editor, you can also do this from the command line:
gsettings reset-recursively org.gnome.Cheese:/apps/cheese
UPD since I don't know when, that gives an error:
Schema “org.gnome.Cheese” is not relocatable (path must not be specified)
Which simply asks to call it without the /apps/cheese path, like this:
gsettings reset-recursively org.gnome.Cheese