The key to the service is to associate the incoming email with an existing Challenge_Comment__c record that the person is replying to (this creates a discussion thread). Perhaps putting the name of the original comment (e.g., CC-11532) in the subject or somewhere in the body? You may have to change the format of the email that goes out to accomidate your code.
Create the following Challenge_Comment__c custom object (disregard the UserProfileFeedId field as not needed):
Create the following Mail__c custom object:
When a new record is inserted into the Challenge_Comment__c custom object, an "after insert" trigger fires (the actual code is attached in the assets section) to add the record to the Mail__c custom object. Another service will eventually pick up this record in the Mail__c object and send it out via email.
Must have 90%+ test coverage. Be clear and concise on how to setup this service and any changes to existing functionality.