How can they not effect the sound

I have three systems, and one of them uses small stand-mounts. One of the tweeters has a small dent. I can't detect any difference in sound quality or volume level compared to the other speaker. I have no explanation, but posted this to confirm what you've read from others.

A small dent in a speaker cone usually doesn't significantly affect sound quality because the cone is designed to flex and vibrate across its entire surface, meaning a localized dent doesn't drastically disrupt its movement, especially if it's only on the dust cap which is primarily a protective layer; the key factor is that the cone material remains intact and can still move freely to produce sound waves. 

Key points to consider: 

• Dust cap function:

  The part that usually gets dented is the "dust cap," which sits on the center of the cone and is mainly there to protect the voice coil from dust - not to contribute significantly to sound production. 

• Cone material properties:

  Speaker cones are designed with materials that can flex and vibrate evenly, so a small dent might not disrupt this movement enough to cause a noticeable sound quality change. 

• Severity of damage:

  While a small dent might be negligible, large dents or tears in the cone can significantly affect sound quality by disrupting the cone's ability to move properly. 

I used to own some wonderful Von Schweikert speakers.  The dome tweeter of one was dented.  On the advice of VS, I used the tube extension of a vacuum cleaner to remove the dent.  The directions were as follows:  with vacuum on and tube held steady, pointing straight at the dome, slowly approach the dome. When you get very close without touching, say an inch or two, it will pop out.  I did and it did.  

Depends where. For a dome tweeter a dent can do a lot of bad things.

The use of a vacuum is a great fix. Also, with some tweeters the dome is removable and you can fix them by pressing from behind. This is the preferred solution with tweeters, as suction in a small area may be hard to control without excess force in the suspension.

Tweeters don't have a "spider" holding the dome in place.  The surround is the only part of the suspension and it comes out when you disassemble the face plate, when manufactured to do so.  That is, with the right screwdriver or Allen wrench the whole thing comes apart and gives you access to the back of the dome.  Not true for mids and woofers I'm afraid. 

That is, with the right screwdriver or Allen wrench the whole thing comes apart and gives you access to the back of the dome.

...and occasionally to the ferrofluid hosted in the magnetic gap, or what's left of it.