Yes, if your home was purchased in 2018, entering the date that you purchased the home instead of the date of the refinance will have no impact on your tax return. The same $750,000 limit applied to homes purchased in 2018 as they do in 2021, which was the date TurboTax was using before you changed it.
If you are using TurboTax Online, you can use a rather roundabout way to see your deductible mortgage interest. Click on Wrap up tax breaks at the end of the Deductions & Credits screen. After answering a few more questions, TurboTax will say Based on what you just told us, itemizing your deductions is best for you. You can click the button below that which says Show me the breakdown of my itemized deductions. One of them will be All deductible interest, which will include your mortgage interest, as well as investment interest and mortgage interest credit certificates, but they are pretty uncommon.
I'm unclear what happened in your update. Do you mean that you deleted them and re-entered them and TurboTax is still coming up with the same answers? If so, good, that means it probably calculated correctly the first time. When you said you removed the second and your refund went down a little bit, yes, that is normal. Your refund should go down when you delete that form since you are no longer receiving a deduction for the mortgage interest reported on that second 1098.
Sometimes, in situations like yours where the refinance is very late in the year, the taxes owed may actually increase when you enter the refinance 1098. This is not common, but it can happen, especially since it looks like you rolled some of the refinance costs into the loan making it have a slightly higher average balance than your first loan.
