If I'm not mistaken, that should be a (possibly tuned) IF transformer belonging to the crystal filter behind it; it's used for impedance matching and (if tuned) improving far-off selectivity. The two slugs seen to the right are adjustable inductors (only to be changed with the right tools, for it's easy to crack the core), and the pink thing at the right is a trimmer capacitor; all of those should be on RF level.
None of all these are related to tone at all. Does either the transmitter or the receiver have a level control? Then crank that up for a bit. You obviously want an effective input level comparable to a real pickup at the guitar amp (keep in mind the signal has to be amplified, modulated (probably FM), demodulated and brought down to a suitable level). Other than that, you have to keep in mind that the input impedance of the transmitter and the guitar amp may be different, and so the interaction with pickup impedance may yield somewhat different results.