find apache-tomcat-7.0.23/ -name "spring*.jar"
should show things like: apache-tomcat-7.0.23/webapps/bss/WEB-INF/lib/spring-beans-3.1.1.RELEASE.jar
apache-tomcat-7.0.23/webapps/bss/WEB-INF/lib/spring-core-3.1.1.RELEASE.jar
apache-tomcat-7.0.23/webapps/bss/WEB-INF/lib/spring-expression-3.1.1.RELEASE.jar
and you need to worry if those version numbers are 3.0.6 or lower. you only really need to worry about the expression language, which is the last one, but i cannot promise it is named the same in other versions.also, this assumes that the project was built with maven or otherwise uses standard jar names. if the jar was hand-rolled and named then it could look like anything... (in which case applicationContext.xml, as suggested elsewhere, at least warns you it's spring).
spring-beans and spring-core are the fundamental building blocks of most Java EE applications and using them in no way causes the aforementioned vulnerability.
The only case that causes this vulnerability is when a JSP page contains this code : <spring:message text="" code="${param['message']}"></spring:message> Any admin can run fgrep or equivalent on all jsps to see if they contain this text <spring:message text="" code="${param
And if you use a templating engine that uses these tags you'd have to trace whether they are invoked anywhere... So it's not as simple as a grep at all.