The New Kadampa Tradition (NKT) does not have portraits of the Dalai Lama on their Center shrines because NKT practitioners are not Tibetan Buddhists and the Dalai Lama is not their spiritual leader. NKT Centers also do not have portraits of him in their entrance halls and so on because he is not their political leader.
How this situation came about was explained by Ven. Geshe Kelsang in 1997 when he was asked why the portrait of the Dalai Lama had been removed from Manjushri Kadampa Meditation Center:
Lama Yeshe was the general spiritual director of Manjushri Center, while I had the responsibility of organizing the daily programmes. We were both very happy to have the picture of HH the Dalai Lama on the shrine because we hoped that the people of Manjushri and HH Dalai Lama would develop a good spiritual connection and relationship. Many times we invited the Dalai Lama to come to Manjushri Centre, although we both knew, even then, that he had rejected the practice of Dorje Shugden. We assumed it was not his real intention because we found it difficult to believe that he really wanted to destroy the practice of Dorje Shugden.
So for a long time we continued to practise Dorje Shugden and kept faith in the Dalai Lama. Then later the situation deteriorated because he intensified his ban on Dorje Shugden worship. I heard that he said in public that those who practise Dorje Shugden cannot be my friend. Then my mind gradually changed, especially as we received criticism from people who were saying that Manjushri Centre had broken its guru devotion to the Dalai Lama because of our continued practice of Dorje Shugden. As his picture was on our shrine, people believed that he was our root Guru — on the other hand because we practised Dorje Shugden people thought we were against the Dalai Lama. Due to this contradiction we received a lot of criticism. In order to resolve this contradiction and to show that the Dalai Lama is not our root Guru we removed his pictures. This is how we came to remove the pictures of HH Dalai Lama.