Not sure what you mean by "claim " it---the stimulus check is not taxable.  You will be asked about it--you will answer whether you received it in 2020 but you will NOT be taxed.  (Edited to include the word NOT)

The stimulus check is an advance on a credit you can receive on your 2020 tax return.  If something went wrong or you did not get the stimulus check this year, you can get it when you file your 2020 return in early 2021—if you are eligible.It will end up on line 30 of your 2020 Form 1040.

https://www.irs.gov/newsroom/economic-impact-payment-information-center-topic-j-reconciling-on-your-...

https://www.irs.gov/coronavirus/coronavirus-tax-relief-and-economic-impact-payments-for-individuals-...

Yes but it's not taxable.  You enter how much you got at the end so you don't get it added to your tax return again.  Or if you are entitled to more it is added to your return.

To enter your stimulus payment in TurboTax, type "stimulus" (without the quotes) in the Search box, then click the link that says "Jump to stimulus."

Just follow the interview ... everyone will see this screen in the Federal Review tab ...

Since the question about the stimulus doesn't happen until the END of the interview the program calculates the credit and includes it in the refund meter  early in the interview ....  but  UNTIL you indicate how much you actually got in the ADVANCE payment it cannot know the correct amount is as  you are not allowed to get it again.   I think the timing of this question is not ideal however the Refund-O-Meter is not to be believed until you have completed the entire interview process.  This is a question we will have to answer a lot I fear just like the "missing" EIC & CTC credits.  

See information from the IRS:

Recovery Rebate Credit | Internal Revenue Service (irs.gov)

my EIP was based on my 2019 AGI.

Will the EIP now be based on my 2020 AGI ??

I think only if you qualify for more.  But they won't take any back if it should have been less.

See these 3 IRS questions on reporting it on your 2020 return

https://www.irs.gov/newsroom/economic-impact-payment-information-center-topic-j-reconciling-on-your-...

@fanfare 

This is like the story of Goldilocks in a way ... for some the amount they got in advance  was too little, for some it was too much and  for others it was just right.     The EIP will be calculated on the 2020 information however if you got too much in advance you don't have to pay it back  but if you didn't get enough then you will get more.  Most people got the correct amount in advance to they will balance out exactly. 

What ever happened to Goldilocks? Did things work out for her? Or did the bears eat her.?

LOL ...Goldilocks ran down the stairs, opened the door, and ran away into the forest. She never returned to the home of the three bears.   Much like the way I do on some of these questions.  

I entered $ 2400 for first check and $ 1200 for second  ( wife and myself )

Income approx  $ 880 k joint

why did turbotax TAX it  ?

You make $880,000 a year?  You need to go to a CPA.

Did you see your refund go down?  You are not paying tax on them.  But Turbo Tax started out by giving you credit for the whole amount so you refund was too high at first.  Then when you entered what you already got the starting refund was reduced or the tax due increased.  You don't get it twice.

Your 2020 return starts out by assuming you didn't get any Stimulus payments so it gives you credit for the full amount.  Then near the end you enter how much you actually got so it only gives you the difference if any.