In Syslog Reporter, what do the Mute and Trim dialog boxes (regex rules) and ‘switches’ do?

Mute and Trim are two types of filters for the information provided under Syslog Report (Mute is also located under the Trap reporter as well). 

Mute: Syslog table omits entries with the keyword specified in the Regex dialog box.
 
Trim: Syslog table only removes the keyword from entries.

 
When you add a word to the mute dialogue box, and click the table button, it will remove all the entries (lines) with that word in it.  

When you put a word to filter under Trim and click the Table button, then it will only remove that keyword from the entries not the entire entry/line.    
The toggle button just means you can leave the regex parameters in the box, but it won't apply.
 

Note:  This doesn't remove the entries from the database, it's just a filter process.