OK.  One thing that would be a dead easy change is to update the code so that it no longer validates the email you enter.  This is a short term work around while we get the app corrected.

Naviagate to setup > develop > Apex Classes

Click "Edit" next to 

GoogleAlertToChatterSettingsController

Comment out lines 33, 56,57,58.  To comment out a line, simply prefix it with a "//" (two forward slashes).  It will look like this -- note that I've commented out the "if () {" and the "} else {}" block but left the other portions in tact.

  public Void updateAddress() { //method to update emailServiceAddress
  // if (emailServiceAddress.contains('.in.salesforce.com') || emailServiceAddress.contains('.in.sandbox.salesforce.com')) {
    List<Google_Alert_to_Chatter_Settings__c> settings = [select Email_Services_Address__c
                                                          from Google_Alert_to_Chatter_Settings__c limit 1];
    //if a record exists, update the address in the record
    if (settings.size() > 0) {
      settings[0].Email_Services_Address__c = emailServiceAddress;
      try {
        update settings[0];
      } catch (DmlException e) {
        ApexPages.addMessages(e);
      }
    }
    //otherwise, insert a record with that address
    else {
      Google_Alert_to_Chatter_Settings__c setting = new Google_Alert_to_Chatter_Settings__c();
      setting.Email_Services_Address__c = emailServiceAddress;
      try {
        insert setting;
      } catch (DmlException e) {
        ApexPages.addMessages(e);
      }
    } // end if/else
    showCheckMark = true;
  // } else { //if the email address does not have the right '.in.salesforce.com' or '.in.sandbox.salesforce.com' domain
  //  ApexPages.addMessage(new ApexPages.Message(ApexPages.Severity.ERROR, 'Email address must be a valid Email Services address'));
  // } // end address check
  }// end updateAddress method

The attachment is a screenshot in case this is easier to understand (but it's of the same code, not an additional change):