I am not surprised.
As soon as you put your hand near to this thing, the stray capacitance will change and the frequency will change as a result.
The antenna is connected directly to the circuit which determines the frequency, move the antenna, change its shape or bring another object near to it and the frequency will change.
C4 is not "optional" it is ESSENTIAL.
The circuit is at best a toy, at worst a piece of junk. I am sorry if this sounds harsh, but that is the reality.
JimB