You're being too paranoid here so apologize to the handyman and let him continue to remove the tile, just have him wear a mask and clean up when done.

Yes, I do know the risks of asbestos causing Asbestosis and potential mesothelioma later in life but here are a few facts from the Mesothelioma center.

• Light, short-term exposure rarely causes disease.
• A one-off exposure from do-it-yourself renovation is not a major risk.
• Asbestos exposure is cumulative, so short-term exposures can add up.
• Not everyone who is exposed to asbestos gets diagnosed with mesothelioma. Even for people who were exposed to large amounts of asbestos, it is rare to develop mesothelioma. While asbestos is the cause of mesothelioma, a number of risk factors make certain people more likely to develop this cancer.

For comparison you're more likely inhale more asbestos walking a busy mile of roadway in a city with stop lights every block, or waiting to have your brakes replaced. Many brake pads and clutches contain asbestos and test have shown 30% of dust in a garage doing brake work is asbestos. The EPA is aware of this and have guidelines to follow if you chose to do your own brake work.

Do's for Home Mechanics:

• Use pre-ground, ready-to-install parts.
• If a brake or clutch lining must be drilled,grooved, cut, beveled, or lathe-turned, use low speeds to keep down the amount of dust created.
• Use machinery with a local exhaust dust collection system equipped with HEPA filtration to prevent dust exposures and work area contamination.
• Change into clean clothes before going inside the home and wash soiled clothes separately.
• Minimize exposure to others by keeping bystanders, as well as food and drinks, away from the work area.

There is no reason for your paranoia, let them finish the job and be done with it. One thing I'll tell you is the black mastic on the floor will never come up and makes it hard to stick anything on it and stay. I've used a product in a gallon can and a paint roller to cover the black mastic which will allow new flooring to stick and stay, but I can't remember the name. In your case sheet vinyl would be a better choice than the peel and stick squares.

I agree with Kevin. It all needs to come up, now. Just take a lot of precautions, or have an abatement team remove. Use regular sheet type vinyl on the floor, not peel and stick floor tiles. Any moisture in that concrete and those peel and sticks will be moving and not look good, and it wont take long either.

Thank you both for your advice! I guess I am wondering specifically about LVP: can we use that instead of the peel n stick now?

I would believe you can but read the installation manual for the product you plan on buying first, but I haven't had an opportunity to use the stuff to know it's limitations. You said you have sloped drains, (common) and with sheet vinyl and soft vinyl squares it will conform to the slope. With rigid commercial square vinyl a heat gun was needed to soften the vinyl to lay down and conform to the slope around drains.

Since I haven't used LVP I'm not sure it a heat gun would soften LVP to conform and hopefully someone with hands on knowledge can answer your question.

lvp, needs a perfectly level floor.

Building Science Corp. repeatedly warns against using impermeable materials such as vinyl tiles directly on concrete basement floors. Rising water vapour, driven by the pressure differential between the ground and the interior of the basement, can get trapped, causing tiles to lift or discolour.

Thank you all!

Whether or not we go with LVP (or peel & stick), our handyman is recommending that we ensure the floor is even by using self-leveling compound. Leveling the floor around the drain is a different story. I have read that we can raise the drain, or use shims or other underlayment in that area to create a level surface. But that seems out of the expertise of our handyman.

Good question! I am clueless about all of this. Maybe we should use the peel and stick in the laundry area (where the drain is), and then use the nicer LVP on the other half of the space. The whole space is about 12 x 20.

There is a kind of soybean-based solvent that you can use to get the black mastic off. I tried some of it years ago. I believe it was called Beano or something like that. The black mastic is God awful stuff. The process is very slow and time-consuming. You won't die from a one-time exposure to scraping up a few tiles in your basement. It's easier to cover this stuff up than get it off. I have one basement room where I'm considering covering the old vinyl asbestos tiles with carpet squares because it too has an uneven floor.