If you remove I2 then by Le'Chatalier's principle, the reaction will proceed backward to produce more H2 and I2 until it reaches a new equilibrium with a higher [H2].
Now, this is a very complex problem (at least to me it looks like this). Here's how I would approach the problem. Since you can remove only I2, that means the amount of hydrogen atoms in the mixture (whether in H2 or HI) will remain constant. Therefore, if you have 2.343 mol of H2 at equilibrium, you should be able to calculate how much HI you have at equilibrium. From those two values, you can get the number of moles of I2 present at equilibrium. Then, you can work back to find out how much I2 you removed from the system.