If it is an embedded image, then the image will be attached to the e-mail: the image link will reference this and there will be no tracking when it is displayed, because no external site is involved. Although tracking is not involved in the display of the image, if there is an associated link for clicking on an image, there may well be tracking information in this link.
On the other hand, as is often the case, the image may reside on an external web site, and then it often contains tracking information. The image may also have further tracking information within any link called when you click on the image.
Gmail has an option to suppress the display of images from external sites, unless you specifically request it, either for the current e-mail, or for all e-mails from the current sender. Local e-mail clients, such as Thunderbird or Outlook, have similar options, and the purpose is to prevent any tracking resulting from requesting the remote image.
If you use a local client, there is generally an option to view the unrendered source, and this allows you to investigate the source link which loads an image and the target link when you click on it. If you use Gmail's web interface, there is an option "Show original" to do the same.
If you copy the source link for an image, you can usually edit out the tracking information without affecting the image displayed, but this is not always true: sometimes the tracking determines what image will be sent. The best you can do is to try a couple of modified tracking strings and see what image appears, if any.
A couple of extra points:-
- Just because there is tracking information in a link, it doesn't necessarily mean that you are being identified personally: often its purpose is to identify the whether the e-mail has been displayed (the source link), and which image in which e-mail has induced the recipient to click (the target link), so as to assess the e-mail's effectiveness.
- If an e-mail has been sent to multiple recipients (usually in the BCC field) then the same links will be received by everyone on the list, so any tracking cannot identify individual recipients.
- Sometimes the image loaded by a tracking link is invisible, either because it is one pixel square, which is too small to notice, or because it is rendered in the background colour, so just because you don't see anything untoward when you allow remote images it doesn't mean that the display of the e-mail hasn't been tracked.