Hi,
If the transaction between the 2 NGO's is in the nature of free training expenses and does not involve any fees for the same and only reimbursement of expenses is there, then there is no income earned and hence no need to deduct TDS. The question of TDS does not even arise in that case.
In case, there was a fees involved in the training service, then if the training service was within the scope of the charitable services of the NGO and hence falls under charitable activitites, then also, NO TDS applicable in such case.