I've never used TMRpcm...
Is that between the Arduino and amplifier, or do you have powered speakers (with a built-in amplifier)?
I don't know what the PWM frequency is for TMRpcm (I know it's higher than the default PWM) but a 3kHz filter should filter it out, giving you pretty-good analog.
A "chirp" seems odd. A "click" or "pop" when the audio starts wouldn't surprise me. Since the Arduino can 't put-out the negative waveform, the output has to be biased. That means silence has to be at 50% PWM. Whenever that bias kicks-in (when the audio starts, or before the audio starts, there WILL be a pop or some kind of glitch.)
I don't know when that happens with TMRpcm. There might be something in the documentation. Maybe you have to play a silent file first?