I was going to choose ‘‘ignore’’ but I thought that since it’s supposed to be the opposite of ‘‘not to notice’’ I should select ‘‘see’’.
By the way, if you replace ‘‘not to notice’’ with ‘‘ignore’’ then you get ‘‘He pretended to ignore me, but I could tell he was trying to ignore me’’.
not to notice - not be aware of
ignore - to deliberately disregard
The difference comes in the deliberation of the act. The first is not deliberate, the second one is.
The ‘he’ appeared not to be aware of the speaker accidentally, but in reality the speaker felt it was a deliberate act of disregard.
I can see why on first read-through the use of ‘but’ there would lead you to think you should choose an opposite, though. It is tricky.