It seems like car dealerships and car servicing are one of those last great bastions of criminality that everyone sort of knows exists but tends to turn a blind eye to. From the aggressive high-pressure sales tactics to the endless tens of thousands of anecdotal tales about how horrendous some places are. Top that off with repeated TV crews running investigations into service places that charge customers but don't do the service and you realize that barely half a year goes without some corporate chain being exposed.
Personally I'd never take my car to a quick-lube oil-change place again. I've had direct experience of the big US chain (I won't name them but it rhymes with Kwik-e-lube) and the big UK chain (rhymes with Brit-fit). In the US they forgot to tighten an oil filter and it came off on the drive home and crapped out an entire engine's worth of oil on to the road (fortunately, I managed to save the engine). In the UK I had an exhaust done which came off on the motorway driving home and went through the window of the car behind me. There are plenty of cases where similar events have happened, people's engines have been ruined and the brand or chain in question has not taken responsibility for what is clearly their problem.
So what can you do about it? Depends on whether you trust the places to do the work they say they'll do. It's sad that this question even has to be asked. But the quickest way to know for sure is to mark the item before you take your vehicle in. A little blob of silver paint, or scratch the item in a unique place with a screwdriver - something you can use to identify it if it's still on the car once they say the work is done.
Be careful of the up-sell. Most lube places don't make their money on the basic oil change. You'll go in asking for whatever they're advertising, and instantly they'll try to upsell you to the 'premium' oil. I guarantee it. Then they'll likely start with air filters, windshield wipers, brakes being too worn, brake fluid being old, power steering fluid being old (in both cases they'll tell you it either smells burned or is the wrong colour) and best of all - the engine flush.
Just don't do it - get the oil change and get out. Then get someone else to check whatever it was they told you needed doing, so you're not being pressured into a spur-of-the-moment decision.
And if they tell you 'legally we can't let you leave without doing your brakes', that's a classic red flag that they're trying to fleece you.
Buyer beware - as always.