"Find Contributions" search does not work properly with GiftAid batches

I cannot reproduce this in the public sandbox because the GiftAid extension is not installed. I reproduced this using CiviCRM version 4.4.4 and uk.co.compucorp.civicrm.giftaid version 2.2

To reproduce the issue do the following:
1) Go to "Contributions ... Find Contributions" and search on any criteria

2) Choose some contributions and then select the action "Add to Gift Aid batch". On the next screen, choose a batch title and click the button "add to batch"

3) Go to "Contributions ... Find Contributions" and search on the filter named " Batch name" and choose the batch from the previous step. Then click the "search" button

At this point you will get NO results from your search. ( The Gift Aid report from the extension works fine)

I have 2 ideas on how to approach this issue:
a) Do NOT list GiftAid-type batches in the "Find Contributions" criteria list of batches.

or
b) Fix the the "Find Contributions" logic to work with Gift Aid batches.

Question:
I am planning to use both GiftAid batches AND Accounting batches, what is the suggested process? At the moment I can add the same contribution to a GiftAid batch AND a different accounting batch. Is this recommended?