As of OpenMDAO V3.4 there is no button to hide them. There is an open issue to add that button though https://github.com/OpenMDAO/OpenMDAO/issues/1363
In the short term, since you are embedding it you can do a bit of CSS hacking to make it work.
If you add the following the CSS:
#solver_tree {
visibility: hidden;
}
then it will hide the solver tree for you.
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