Why is the amount of my 1099-Q income being deducted from the total scholarship amount on my 1098-T? Do I need to re-report the scholarship income from the 1098-T?

Your question is not clear. For example "Original 1098-T=$20,000" doesn't tell us what's in box 1 and box 5.

It sounds like you need to delete all education input and start over.  Don't import; type it in by hand.

There are three things you can do with your Qualified educational expenses (QEE):

1. Allocate then to scholarships (so that the scholarship remains tax free)
2. Use them to claim an education credit
3. Allocate them to the 529 distribution (1099-Q) so that it will not all be taxable

TurboTax allocates QEE, in that order, until you tell it otherwise.

Provide the following info for more specific help:

• Are you the student or parent.
• Is the  student  the parent's dependent.
• Box 1 of the 1098-T
• box 5 of the 1098-T
• Any other scholarships not shown in box 5
• Does box 5 include any of the 529/ESA plan payments (it should not)
• Is any of the Scholarship restricted; i.e. it must be used for tuition
• Box 1 of the 1099-Q
• Box 2 of the 1098-Q
• Who’s name and SS# are on the 1099-Q, parent or student (who’s the “recipient”)?
• Room & board paid. If student lives off campus, what is school's R&B charge. If the student lives at home, only the school's board charge for on campus students. 
• Other qualified expenses not included in box 1 of the 1098-T, e.g. books & computers
• How much taxable income does the student have, from what sources
• Are you trying to claim the tuition credit (are you eligible)?
• Is the student an undergrad or grad student

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Qualified Tuition Plans  (QTP 529 Plans) Distributions

General Discussion

It’s complicated.

For 529 plans, there is an “owner” (usually the parent), and a “beneficiary” (usually the student dependent). The "recipient" of the distribution can be either the owner or the beneficiary depending on who the money was sent to. When the money goes directly from the Qualified Tuition Plan (QTP) to the school, the student is the "recipient". The distribution will be reported on IRS form 1099-Q. 
The 1099-Q gets reported on the recipient's return.** The recipient's name & SS# will be on the 1099-Q.
Even though the 1099-Q is going on the student's return, the 1098-T should go on the parent's return, so you can claim the education credit. You can do this because he is your dependent.

You can and should claim the tuition credit before claiming the 529 plan earnings exclusion. The educational expenses he claims for the 1099-Q should be reduced by the amount of educational expenses you claim for the credit.
But be aware, you can not double dip. You cannot count the same tuition money, for the tuition credit,  that gets him an exclusion from the taxability of the earnings (interest) on the 529 plan. Since the credit is more generous; use as much of the tuition as is needed for the credit and the rest for the interest exclusion. Another special rule allows you to claim the tuition credit even though it was "his" money that paid the tuition.
In addition, there is another rule that says the 10% penalty is waived if he was unable to cover the 529 plan withdrawal with educational expenses either because he got scholarships or the expenses were used (by him or the parents) to claim the credits. He'll have to pay tax on the earnings, at his lower tax rate (subject to the “kiddie tax”), but not the penalty.

Total qualified expenses (including room & board) less amounts paid by scholarship less amounts used to claim the Tuition credit equals the amount you can use to claim the earnings exclusion on the 1099-Q. 
Example:
  $10,000 in educational expenses(including room & board)

   -$3000 paid by tax free scholarship***

   -$4000 used to claim the American Opportunity credit

 =$3000 Can be used against the 1099-Q (usually on the student’s return)

Box 1 of the 1099-Q is $5000

Box 2 is $2800

3000/5000=60% of the earnings are tax free; 40% are taxable

40% x 2800= $1120

You have $1120 of taxable income  

**Alternatively; you can just not report the 1099-Q, at all, if your student-beneficiary has sufficient educational expenses, including room & board (even if he lives at home) to cover the distribution. You would still have to do the math to see if there were enough expenses left over for you to claim the tuition credit. Again, you cannot double dip!  When the box 1 amount on form 1099-Q is fully covered by expenses, TurboTax will enter nothing about the 1099-Q on the actual tax forms. But, it will prepare a 1099-Q worksheet for your records, in case of an IRS inquiry.

On form 1099-Q, instructions to the recipient reads: "Nontaxable distributions from CESAs and QTPs are not required to be reported on your income tax return. You must determine the taxability of any distribution." 

***Another alternative is have the student report some of his scholarship as taxable income, to free up some expenses for the 1099-Q and/or tuition credit. Most people come out better having the scholarship taxable before the 529 earnings.