In my survey, I had a screening criteria but later it turned out that some participants that were supposed to be excluded got past it. I only figured out later that they were supposed to be excluded based on answers to their later questions that made it obvious that they should have been screened out in the first place. This happened with 2 such participants.
When I run and export the Statistics on LimeSurey, is there a way I can specifically exclude the responses of those two participants?
First of all, the "statistics" of Limesurvey do not substitute a real analysis. They are actually just a tool for quick reporting during the field time, to get a feel of the direction things are going. Nothing that I would base my real analysis on. I would always export the data (as SPSS, Excel, or CSV file) and analyse in a tool that is made for analysis. Limesurvey is a tool mainly for data collection and its data analysis capabilities are very basic.
That said, I don't think that you can run statistics only on a specific subset of responses. But if these should have been screened out anyway, you could just delete them from the response table and they won't impact statistics anymore.
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Note: I answer at this forum in my spare time, I'm not a LimeSurvey GmbH employee.