The harmonics are expected because the red fob transmitter is designed to operate at multiple frequencies as there is no band-pass filter in the schematic. You can only see the impedance matching circuitry, DC-block caps, and the pull-up at the RF_out pin. Using a spectrum analyzer, the measured values are:
- 434 MHz -39 dBm,
- 868 MHz -58 dBm,
- 1302 MHz -62 dBm,
- and 1736 MHz -74 dBm.
Note that the power level difference between the fundamental frequency and the harmonics. It can be noticed that there is a difference of 20 dBm between the fundamental and the second harmonic. Before resolving the harmonics issue, you should first ask how these harmonics affect a product, considering that the power levels are minimal. Do these harmonics violate any government wireless regulations? If the harmonics affect the product or violate wireless regulations, add a low-pass filter or a band-pass filter in your circuitry. The filter is normally added right after the RF_out pin of U1 and before L5. The added filter might slightly affect the impedance matching's scheme of your circuitry.
Part number 0400LP15A0122 by Johanson Technology Inc. is an example of a Low Pass Filter.