Most of the magic I perform can be inspected, but I never let them. No matter what, heres the thing, if they want to check the deck, you're doing the trick wrong. No offense. I often offer people the deck, and they simply do not want it. Sometimes you get grabby spectators and you cant do anything about that, right? WRONG!! You should be able to spot a troublesome spectator, if you're table hopping you could simply be on the other side of the table, (Great advice I got from Mike Close). And if you have to be a foot away from a troublesome person, only perform inspectable magic for them.
I agree with most of this, but would like to add a few points.
The more you perform, the better you will handle your spectators. Grabby spectators are annoying, but tend to show up when you break the barrier between you and the audience. This is more likely to happen when you are new and performing for a group of kids at school or your place of work, or if you are just someone who starts doing magic on the street for the heck of it. You are just part of the crowd. They can interrupt you; they can mess with your stuff, etc. You are one of them. You can do some fantastic magic when you break down the barriers between you and the crowd, but it comes with a price. However, when you are the “hired” magician, or you are doing a show on the street and you look like a "pro", you are less likely to see this "gabbiness." It still can happen, though. It is difficult to teach someone how to handle bad spectators, but some of the advice given is fine. Experience is the best teacher.
It is often said, though, that a magician who has a spectator who wants to look at his or her cards or props is a magician who has to improve their presentation. In other words, it is the magicians fault. Although I agree that presentational skill will help your handling of the really bad spectators, and you should try to stop the grabby spectators, I think in general, if you have spectators who do not
want to look at your props, it may be a sign that you need to improve your presentation.
If you do a snap change and people do not
want to look at the card, then you did a crappy job. They may be too polite to say anything, and there are ways to convince the spectators that you are using real cards which may keep them from grabbing, but they should want to touch and examine the source of the magic. That does not mean that you want to get into the habit of handing out the cards on a whim, but people will want to look. I like to do tricks that the spectators can handle if they want. I don't like handing things out just because they ask, but for many card tricks the cards end up on the table and can be examined. The specs seldom do, but they could.
For an effect like Invisible deck, I will usually do this separate from other card effects. Since they see a fanned out deck with one face up card, and because they can pull out the reversed card, I rarely have to deal with the spectator who says, "Let me see the cards!" Why would they? It is a mental magic effect. All I do is show a reversed card. The magic is not in the cards, but in my ability to predict their choice. If I do Fechter's That's It, they see the selected card put on the table (along with several others) and then it ends up in my hand. They always want to look at the pile of discarded cards to see if I have a dupe there. They just saw me put it there. If they don't
want to look, then they are probably trying to get away from my boring presentation.