I'm wondering what some of the pros and cons are for them paying off the mortgage.
As far as I'm concerned there aren't any cons. I am a big fan of owning a home free and clear after my working years are over. The title of this forum is Mortgages, Refinancing, and Foreclosure so I'll be happy to give you my opinion, which is: Sell the rental, pay off the home, avoid tenant hassles, mortgage company vultures, and 22 years worth of interest that sucks you dry and is probably no longer tax deductible.
Watch your bank accounts grown each month that you get to keep your retirement income instead of handing it over to the mortgage company.
You'll pay some capital gains tax on the rental. Big deal. It's a fact of life. There really isn't a tax issue on your main home unless you sell it for more than a $500,000 gain over your purchase price.
Then there is the psychological factor. After 20 years of hassling with mortgage companies (constant mistakes month after month) and hassling with tenants, I sold my rentals in 1998 and bought a house for cash. A month later euphoria set in when I opened my check book, saw that the last two paychecks were still there and I never had to make a mortgage payment again. My savings grew month after month. I paid off a new car loan in two years. Two years after that I bought my next new vehicle for cash. I retired at the age of 60 with a lot of money in the bank. I took Social Security retirement at 62 and it pays all my bills.
When I decided to downsize this year I bought a second house for cash without having to be under the gun to sell my other house.
So, yeah, if you can pay off your mortgage and still have a comfortable cushion of savings whether you sell the rental or not, I'm all for it. I would sell the rental, though, and take the equity. Don't fear the tax man. Think of it this way. If your gain is $100,000 and you have to give the government $20,000, you're keeping $80,000.
Who knows, when you decide to downsize you may also be able to buy your next house for cash and take your time moving.