I'm sure I've read somewhere that after Rasputin's death Anna Vyrubova found Aleksei crying in his room sobbing "who will help me now" I just don't remember where I read it.
This is from Anna's Memories of the Russian Court
Alexei usually defended all offenders, yet when the day came when his parents, in deep distress, told him that Father Gregori, that is, Rasputin, had been killed by members of his own family the boy's grief was swallowed up in rage and indignation. "Papa," he exclaimed, "is it possible that you will not punish them? The assassins of Stolypin were hanged."
OTMA in general seem to have gone to Vyrubova's house quite a lot regardless of whether Rasputin was present), but I can't find a single photo of Aleksei there. That strikes me as rather odd...
According to Gilliard "from January 1st, 1914, to the day of his death in December, 1916 Rasputin only saw Aleksey Nicolaievich three times).
The children saw Rasputin when he was with their parents, but even at that time his visits were infrequent. Weeks, and sometimes months, passed without his being summoned to Court. It became more and more usual to see him with Madame Vyrubova, who had a little house quite near to the Alexander Palace. The Tsar and his heir hardly ever went there, and meetings were always very rare."