When you "cash out" on refinancing rental property, the interest on the cash out amount is "NOT" a deductible rental expense. Period. Here's a simplified example.
You refinance a rental property in 2019 and at the time of the refi you owed $50K on the original loan. You refi for $100K, then use $50K to pay off the original loan and the other $50K you put in your wallet. With this scenario, only 50% of the mortgage interest on the new loan is deductible as a rental expense on the SCH E for the life of that loan. That's it.
Now lets say you used $10K of the cash out amount to improve the rental property and pocketed the remaining $40K (or did something else with it not related to the rental property). That would mean you can claim 60% of the mortgage interest on the new loan over the life of that loan, as a SCH E expense.
What you do with the remaining cash-out amount has no bearing on the SCH E. Weather you can claim/deduct the interest on it depends on what you do with it. But it won't be a SCH E expense.
