The word shrink is often slang for a psychiatrist or clinical psychologist.
a clinical psychologist, psychiatrist, or psychotherapist.
In all of the online references to "shrinklette," it seems to refer to someone who is not a professional psychologist, but an amateur. It's possible the author here is questioning whether their students are sincere in desiring to learn and understand psychology, or if they are merely amateurs looking to meet the educational requirements for a job as a clinical psychologist.
I was unable to find the original text on Google books, which would help to clarify whether the term refers to psychologists-in-training or some other field of students.
For instance, I saw several references to "shrinklette" with reference to critics of the controversial family and marriage counselor Dr. Laura Schlessinger.
A few collected uses:
They hate it when the impertinent shrinklette exclaims, “At least a prostitute gets paid!”
Those of you few who knew Dr. Ding when she was but a mere shrinklette in short pants will recall my 1990s-era fascination with the art and life of Frida Kahlo.
The second reference is from a psychology blog referring to a psychologist in their younger days.
A more common term that can be found frequently on blogs and even reputable books is shrinkette.
Here is an example from Beyond Anne Frank: Hidden Children and Postwar Families in Holland by Diane L. Wolf:
So it seems to be a combination of shrink and the suffix -ette, which OED describes as:
1 a. Forming nouns denoting small or brief examples of the thing denoted by the first element, as diskette n., essayette n., kitchenette n., towelette n., etc.