"...don't you have to install the program... in order to be pestered?"
Probably not. I cannot be certain, but I suspect this program implements a dated spammer tactic of assigning HTML content to emails that sends GET requests upon being opened.
For example, if I send you a message with an HTML image tag that directs you to my site (www.mysite.com/some_image.jpg), your email client will probably automatically download it. Most email clients display the image automatically, just like browsing a webpage.
What is really happening is that the email client is sending a GET request to a server. This can of course be logged. What spammers do is attach a unique ASCII code to the GET URL (in my example the image's filename) and correlate this with the address to which the message was sent. So if I want to track you, I generate a unique ID and send that ID only to you, attached to an image (in this case). When your client opens/views the message, that GET request is sent with the unique ID to my server and I know you viewed it, when, with what client, at what IP address, and at what email address.
This can be done without images or with them hidden in an invisible frame. It's common to see an invisible iframe with a 1x1 blank gif. This is a different from the feature that allows a sender to be alerted. This cannot be done with just two users and their email program - it requires a web server. It also requires that the HTML be parsed.
There most certainly is a way to block this. Clients like Mozilla Thunderbird block external requests by default. You can also find the offending company's IP address or domain and block that. But the real answer is for the email clients to change their behavior.
Again, I can only *assume* this is what the service in question does. It's probably written as a COM+ object.