Yes, it is important. Ohio only taxes income sourced in their state. Unlike New York, they consider your wife who telecommutes from out-of-state to be performing services in her home state, not Ohio, even if it was for an Ohio company.
This means that if your wife never worked in Ohio and telecommuted full-time, you should not allocate any of her income to Ohio and should receive a full refund of the amount that was withheld. Ohio still withholds municipal taxes for telecommuters which you may see in Box 14 or 18-20 of her W-2. You won't get those back.
Although this sounds like good news, it really won't make much of a difference on your total taxes. If you had to pay in Ohio, New York would have given you a credit for how much you paid. Now that you don't have to pay Ohio, you won't get the credit in New York and will just owe New York more.
