That is a great question Keannu. It appears that there is a longstanding debate on this. Oxford English Dictionary has a nice description. Merriam-Webster discusses it a bit as well but I don't see it showing in the online version. I think Oxford's discussion is easier to follow though.
Regardless of what we call "than," I would include "to" in "to get" to maintain parallel structure with the counterpart in the comparison ("to do"). Indeed, the sentence would seem incorrect without the "to" in "to get."
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