Can you be more specific in your question regarding MailNotificationTask? Not sure what you're asking...
So I was modifying this Java class for my Customization. Am I in the right track atleast?
Kinda. I hope that by "modifying" you either mean "subclassing" or "copied as the starting point for my own", with a preference on the latter since the OOTB one could change without notice.
I am not aware of the MailNotificationTask class that comes with TeamSite - ours is completely custom.
Check this file "MailNotificationTask.java" under this path/local/config/lib/content_center/customer_samples_src/src/com/corp/customThanks
Right, it's OTB source sample. Unless you've compiled it yourself you will not find bytecode "MailNotificationTask.class" File.