I assume all the 250 files are in the same directory and follow the same naming pattern. If that is the case, you could do,
for i in "$remove"*;do mv "$i" "${i#"$remove"}";done
Testing
ls
no_responseEvent_2002.02.07.03.15.56.970
no_responseEvent_2002.02.07.03.15.56.972
no_responseEvent_2002.02.07.03.15.56.971
no_responseEvent_2002.02.07.03.15.56.973
Now, after I run the for loop, I get the output as,
remove=no_response
for i in "$remove"*;do mv "$i" "${i#"$remove"}";done
ls
Event_2002.02.07.03.15.56.970
Event_2002.02.07.03.15.56.971
Event_2002.02.07.03.15.56.972
Event_2002.02.07.03.15.56.973
References
http://www.commandlinefu.com/commands/view/2519/uniformly-correct-filenames-in-a-directory