To answer your question/s, I have to go into a further analysis of the sentence
concerned - They arrived home to find that the house had been burgled.
Invariably, we go home with a purpose: to eat, to sleep, etc., and in the above
case, to find (something). That is a single idea (a unit by itself) and you don't
break it unless you go into parsing (which is a separate matter) or there are
(within the sentence) extensions by way of adjective/adverb phrases/clauses,
etc.
"To find" is a qualifying infinitive performing the function of an adverb of purpose
modifying the verb "arrived".
Now, let us look at the defination of a "non-finite clause". It's simply a
subordinate clause whose verb is non-finite.
I'm sorry to say that your lecturer's treatment is against the defination because
"had been burgled" is a finite verb (in the passive voice).