stretch your eyes
This is a phrase that I came across in the Macmillan Proficiency Testbuilder:
'Can't you just tell me?' Lisa pleaded, but Pete jutted his chin and said he was only obeying the rules. Lisa stretched her eyes at him. She had been brought up to be wary of anyone who believed in rules.
I have never encountered the phrase "to stretch your eyes at someone" (legs, arms - yes, but eyes?). My first guess was that she gawked or stared at him. Then I realised she probably put the tips of her fingers to her lower lids and literally stretched them down to make fun of the man's attitude. Do I understand correctly? This seems like really odd behaviour, though, considering Pete is her teacher.
"Stretched her eyes" certainly isn't standard usage. I thought at first it must mean she widened her eyes, but the meaning closest to that in the Oxford Dictionary is
Straighten or extend one's body or a part of one's body to its full length, typically so as to tighten one's muscles or in order to reach something.
But you can't straighten or extend your eyes to their full length. So it must be this second sense of 'stretch' that the writer had in mind:
Cause (something) to become longer or wider by pulling it.
In which case she is, as you said, using her fingers. Yes: making fun of him. Pulling a face. (Literally!) It is awkwardly written though. It would be clearer to say, 'Lisa looked at him, pulling her bottom eyelids down'. (By the way, I don't think she would do it if she had been "brought up to be wary of anyone who believed in rules." The use of the word wary is clumsy, I think.)
And it is cheeky of her. But she wouldn't be the first to do it to a teacher.
"Stretched her eyes" is not a common phrase, which means that its interpretation is simply what the words straightforwardly mean.
It's conceivable that it means to stretch your eyes (or the area round your eyes) with your fingers, but it could also mean to do the same thing just with facial muscles, including raising your eyebrows and lowering your cheek muscles.