Just so (that)~

The girl refused to dissect the frog because she couldn't bear the thought of wasting a frog's life just so some student could cut up the body.
[Source: Reading for Results Ninth Edition by Laraine Flemming]

I think "just" just modifies the conjunction of purpose "so that" and that "that" is omitted in "so that."
I'd like to know my thought is right.
Thank you in advance for your help.