It would be helpful to know which reporter mice you have available, and which parasite you're studying; if this is just a general question about reporter mice or a particular set.  there are so many that without a few more details, this is a difficult question to answer.

For example, if you wanted to enumerate the T cells responding to flu, and you didn't care what kind of response they make, you could make a reporter mouse whose T cells light up when they activate CD69.  a floxed stop on the reporter color, driven by cre on a CD69 promoter would permanently color the responding cells, whereas a construct with the color on the CD69 promoter would color them temporarily.

If you wanted to know what kind of responses a particular parasite drives, then you could use reporter mice whose cells become colored when they make particular cytokines.  or you could simply look at the classes of antibodies the mouse makes (without having to use a reporter mouse). 

So it really depends on what question you're asking

I think that this example would be very usefull, Dra Paula Licona and Dr Richard Flavell made these experiments with IL-9 reporter mouse to study immune response to parasites.

Article Th9 Cells Drive Host Immunity against Gastrointestinal Worm Infection