You are correct, the majority of users do not know what a TLD is or probably even care.
I suppose that it depends on what kind of customers that you have, but my experience with my customer base is that they would probably not click on something that looked out of the norm to them because they might think it is a scam or something that they have heard about on the news.
Also, I am thinking of it in terms of your customer remembering your site address into the future. Let's say they click on your site because you rank high, look at the info and then bounce. How many of them are going to remember the TLD if they want to come back to the site via direct entry into the navi bar? There will be a certain % (I think it would be high) who would type in yourdomain.com instead of yourdomain.company
I have seen this many times with close matches to domain names - people come to the site, look at it, then bounce. They come back 2 weeks later via a direct entry into the navi bar, except they enter a slight variation of the actual domain name because (I suspect) they remember that they visited a site they liked, but cannot totally remember the exact address so they do their best. That is why generally if possible, we grab close variant domain names and forward them to the main domain with GA parameters for tracking. It always amazes me at how much traffic we get monthly from people entering in the close, but not exact, domain name in the navi bar.