Since Kolmogorov Complexity is specified in terms of lengths of programs, that means the KC between two different pairs of encodings can differ at most by a constant amount (the size of the program that converts back and forth).
The above is a bit handwavey, there are details you can tighten up (Is it the program size or something smaller? The program length in which encoding?), but heuristically that's why theorists can talk about "the" Kolmogorov complexity without getting bogged down in with pesky encoding details.
It's also why we usually don't worry too much about the fine details of Turing Machines (alphabet, etc.), since you can generally emulate one sort of Turing Machine pretty easily with a short program written on another.
If your Turing machine can only print out zeros and ones, there's no program which can get it to print out "ABC". So it cannot specify a conversion between a language whose symbols are {0,1} and a language whose symbols are {"A",B","C"}.
It could specify a mapping between one binary string and another binary string, but it can't even print out "ABC" so how could it possibly specify a conversion?
This is elementary guys.
Sure, you can object that the encoding is "outside" the TM, but for the purposes of discussing complexity these objections are pretty trivial, again for the same reasons (whatever encoding you pick the conversion process is a program you can write down, and once you write it down it means the Kolmogorov Complexity is the same between different TMs up to the length of whatever encoding/decoding program you come up with).
Put another way, a TM with alphabet is {0, 1} is technically not the same as the TM with alphabet {A, B}. But it's obvious to us that the TMs are equivalent.
E.g., make the machine print out pixel values for a large screen. The screen can display Chinese characters in canonical ways.
