I assume that your former airline sent you a 1099-MISC that set a taxable value to the amount of free travel that you enjoyed for other passengers with you (spouse, kids, travel buddy, etc.).
This is known as an imputed tax, that is, a tax on a something that you received that has some value but which you did not pay for.
It appears that how this is handled varies from airline to airline. See http://www.rafa-cwa.org/Costs-and-Imputed-Taxes for one example (United).
I would suggest that you contact your union (if you still can) and ask them about the airline's imputed tax policy.
If you are told that this is indeed taxable income, if the amount of $3,722.35 is in box 3, then in TurboTax go to Federal->Wages & Income->Other Common Income and click on "Income from Form 1099-MISC".