This is YOUR rental so it belongs on your income tax return not your parent's. The fact you give them money from the net is considered a gift to them which is not income to them nor deductible to you.

Now  if you give more than $16K per person per tax year you may need to file a gift tax return separate from the income tax return. 

I agree with @Critter-3.

Further, you need to be cautious about income(loss)-shifting to relatives who may be in a lower(higher) marginal tax bracket (which is really frowned upon by the IRS).

you and your spouse own the property. who is on the mortgage is irrelevant.  as others have said it's your income and a gift to your parents. if your parents have been reporting the rental in previous years then the wrong party reported it. Even worse the depreciation deduction would have been on their return. when the property is sold you'll have to recapture the depreciation deduction that went on their return.  consult a tax pro in this situation. 

Thank you All for the reply