Why Lashkar-e-Taiba denying responsibility for attack on Amarnath pilgrims?

On Tuesday, Jammu and Kashmir police linked Lashkar-e-Taiba (LeT) to Monday’s attack on Amarnath pilgrims, in southern Anantnag district. But without wasting any time, on the day itself, Lashkar-e-Taiba strongly denies the charge and sought to blame the killings on Indian intelligence agencies.

Some Media reports see this denial a result of International pressure on LeT.

Why will any terror group, with no reputation at all, be weary of such International pressure!

Thus this reasoning seems highly unlikely.

In addition, if the investigating agencies see Monday’s incident as a well orchestrated one, then why will a terror organization plan and execute a terror act, and not own the responsibility later on?

… Why will a terror organization not take responsibility of an act of terror, when its very existence relies on it?

What may be the reason?