I had never seen this until this project based on Magento ver. 22.214.171.124 or, did I not realised before :)
I tried to turn off google checkout by Disabling module at:
System -> Configuration -> Advanced -> Disable Modules Output -> Mage_GoogleCheckout
But, that didn't help. So checked another location to disable and found another location and turned off all google checkout *:
System -> Configuration -> Google API -> Google Checkout -> Enable
Still it was appearing on layered navigation. So, looked on the final location at:
Catalog -> Attributes -> Manage Attributes -> enable_googlecheckout
Here I set "Use In Search Results Layered Navigation" to NO.
Yohooo! finally it's gone from my layered navigation on the sidebar.