No, you can't eliminate it. The guests are not consumed (in the sense of destroyed), but merely incorporated into the complex. [G]_{0} is the total concentration of G in the solution, whether as free G molecules or in the complex.

What that means practically depends on how the experiment is performed, which you have left vague. You say it's a titration, so you are adding something to something, and concentrations will be changing.

For example, suppose you have an initial volume V_{0} of a solution of H of initial concentration [H]_{i}, and titrate it with a solution of G of concentration [G]_{i}. When you have added V_{1} of the G solution, the total volume V_{2} = V_{0} + V_{1} and

[H]_{0} = [H]_{i}*V_{0}/V_{2}

[G]_{0} = [G]_{i}*V_{1}/V_{2}