Thanks.
I cannot do anything with the REL button. I guess that since the meter normally shows zero, and not a negative value, using REL just subtracts this zero, so nothing changes. It seems that my (particular?) device not only compensates for its intrinsic capacitance, but it also over-compensates. Adding 220 pF cap helps. Then I can measure even single digit pF caps.
So another question is: would soldering the additional cap inside the meter affect other measurements? (like V_AC or Hz, which are on the same socket?)