Your stimulus is not taxed and does not reduce your refund. But if you do not correctly enter the amounts of stimulus money you received already, the software can add stimulus money that you are really not eligible to receive to your refund--making it seem like you are getting a bigger refund. But then the IRS cross checks and recalculates when they see how much you already received.
Make sure you enter the amounts you received for both EIP payments in the recovery rebate credit section. Then see if there is anything on line 30 of your Form 1040. Any amounts you are still eligible to receive should show up on line 30.
Click on Tax Tools on the left side of the screen. Click on Tools. Click on View Tax Summary. Click on Preview my 1040 on the left side of the screen.
No ... quite the opposite. If you did not get all the stimulus money you are entitled to using the 2020 information then the missing money can be added to your refund.
What can be confusing in the program is that the credit for missing money is added to the refund in the beginning until you tell the program at the end of the interview how much stimulus money you got in advance and the refund is adjusted accordingly. So if you got both of the first 2 stimulus payments of $1200 + $600 and you tell the program you got those amounts when asked then the refund meter should drop by the same amount.