General observations first. You called it a transmitter, I call it an add-on amplifier. A transmitter is usually a more complete combination of modulator and amplifier. But I'm nit-picking. On my initial look, the receive path is switched through S1 but I don't see anything to drive S1, so perhaps it is just a manual bypass switch?
Alternatively, the path through L1, C2 and C9 may be the receive path. Clearly the diodes are there to perform a crude form of rx/tx switching. For analysis, assume that rx signal voltages are too low to bias the diodes, whereas tx signals always are large enough to bias the diodes.
Bad design is shown by allowing the bias voltage through R1 to appear on the output antenna connector when S1 is in bypass. Then again, maybe this is intentional to provide bias to something further up the antenna line? I also believe it is bad design to couple back to back rectifiers to an output network to any degree as these will generate harmonics and harmonics should be avoided near the antenna terminal.
One way to conveniently analyze the design approach is to understand the mosts common design procedure for matching circuits such as these, and that is using the Smith Chart. You can find many online references to how to use this tool. Analysis of the LC networks may start by assuming that they are trying to make the S22 of this system as low as possible in a 50 ohm system. In other words, perhaps you can assume that the matched impedance at ANT is 50 ohms. Using a Smith chart, you can work backwards through C6+C7, then L4 then L3 to arrive at a possible output Z for the transistor. Same sort of procedure can be used for the input network, only in the opposite direction (on a smith chart, direction is important).
Again, I caution that looking at a matching network as some sort of filter can be misleading as we are not so much interested in resonances as we are in the ability of each reactance to shift the impedance. Make no mistake, ultimately the matching network does perform some filtering as well, but that is not its main purpose. It is an impedance shifting network first and foremost.