Anchoring
Any number you are exposed to before making a numerical estimate drags your estimate toward it, even when the number is transparently arbitrary and irrelevant. The effect survives being warned about it. It operates both as a priming effect on System 1 and as insufficient adjustment by System 2.
In real life
Ask people whether Gandhi was older or younger than 144 when he died, then ask for their estimate — the estimates come out far higher than from a group anchored on 35. Everyone knows 144 is absurd; the anchor works anyway.