My favorite rule: NEVER, EVER, EVER allow someone you don't personally know, to access your computer remotely... EVEN Apple. If I have a problem SO BAD that someone else needs to fix it... I'm taking it into the Apple Store.
While there are no viruses for OS X, there is malware, and one of the easiest ways to get it, is to allow a stranger to remotely access your computer.
My best guess is that he had your daughter install TeamViewer so he could access it. As long as that's still in her Applications folder, I wouldn't trust it.
Download AppZapper (http://www.appzapper.com) - It's a free trial. I use it, you can trust it.
Install AppZapper and use it to remove TeamViewer and its preference files.
Being as your Mac is brand spankin' new... DO NOT be afraid to call Apple 1-800-MY-APPLE (800-692-7753). If you got it at an Apple Store, make an appointment with the "Genius Bar" to have them take a look at it A.S.A.P.
Lastly, ANY TIME OS X asks you to Quit an application... press (⌘+tab) to see everything that's running. Pressing "tab" again will cycle through the icons of the open apps. Once the one you want to quit is selected, press (⌘+Q) to Quit it.
Thanks for your advice, we did call Apple Care (bought the three year contract), the guy said this case is not unusual. You google something like "adobe tech support" and you find websites that pay Google a sponsorship fees to be at the top of the list. Then you call them in good faith, they bring up various screens and tell you that your computer has a problem and try to sell you a service of some kind. The one she picked has telltales on the homepage that it was not legit, mangled syntax, misspellings, she just wasn't paying attention.
Apple guy asked her specifically if the tech downloaded anything other than her end of TeamViewer, she said no. He thought she was probably okay, just said watch and see if computer begins behaving unexpectedly. She had already deleted the viewer and changed her login password after the "Adobe" tech call. TeamViewer isn't in her Application folder.
We did buy the computer at an Apple Store, hadn't thought about the genius bar in the back, will certainly bring it there and see if there are any leftovers they can find.
Also appreciate the tips on the AppZapper, and how to quit applications that run in the background.
At my work and home all the computers are Windows, this is first Mac, so I am not familiar with Mac OS, neither is daughter, so we are both learning. I'm thinking we should get a Dummy book to speed up our learning curve
The "Dummies" books are written by PC people. I wouldn't recommend them. Try "The Missing Manual" for OS X: OS X Mavericks: The Missing Manual: David Pogue: 9781449362249: Amazon.com: Books
David Pogue is a "Mac God". I first learned OS 10.2 from his book for it in 2003,