Hopefully, you mean Tomcat 7.0.40 or 7.0.41. If not, upgrade.
Okay, so you want to be able to contact a particular URL and *not* have the last-used timestamp updated? Do any of the servlets that react to those URLs try to call request.getSession()?
If you are operating in STRICT_SERVLET_COMPLIANCE or ACCESS_SESSION mode, then you will not be able to disable this update. If you are not operating in either of these two modes, you may be able to do it, but you will have to write your own software to:
a) track sessions - probably an HttpSessionListener
b) give access to those tracked sessions without calling getSession - probably using a Filter and an HttpServletRequestWrapper