Setting RF frequency by putting screwdriver into coil
Screwdrivers are usually made of ferrous metals (various steel alloys containing iron.) 

As such, when brought near to or inserted in the interior of an air core inductor, they will increase the inductance of the coil.

Whether that will change the frequency of an oscillator (or in your case, transmitter) depends on what the coil is doing in the circuit.

If it is a choke to keep RF from going back out over the power supply, then changing its inductance won't change the transmitter frequency.

In the circuit you linked to (see below,) the inductor is part of the LC tank that sets the frequency of the oscillator.  Changing its inductance should noticeably change the frequency of the oscillator.

An alternative to poking a screwdriver into the core of the coil would be to add a loop to the coil (permanenly increasing its inductance.). Then you can tune the circuit by pushing the windings apart to lower the inductance.  Once you have where you want it, you just leave the (now slightly mashed) coil as it is and the frequency will stay (pretty much) set.



Variable inductors work in a couple of different ways.

Most variable inductors have a moveable slug of ferrite.  It has screw threads, and rotating it moves it into or out of the coil.  More of the slug in the coil is higher inductance.

I have also seen (and tuned) circuits in which the inductor had a brass slug as a core.  In these inductors, moving the slug into the coil would DECREASE the inductance.

That is the opposite of what you usually expect.

I have read that aluminum reacts much like brass, but I have never seen a variable inductor with an aluminum slug.



Here's the circuit that Cagri was trying to tune:



L1 is part of the LC tank that sets the frequency of the oscillator.