To confirm or deny what I surmised about the transmitter frequency, you could try consulting the datasheet of the 8 pin IC that I have circled in red on the photograph below.
I couldn't read the type number of this IC, it is obscured by the transparent plastic ring.
Could you tell us what it is please?
Also try measuring the length of the track that I have coloured yellow, which I believe is the antenna. I'm predicting it should be close to a quarter wavelength at the transmitter frequency, which is 300/(433.92 x 4) metres = 173mm.
