verstehen = infinitive, but also (here) 1st pers. plur. present tense verstanden = past participle of verstehen (and also 1st and 3rd pers. plur. past tense)
Thanks. I can see now that I got the wrong part of the verb - however, I feel I did get the right verb, and so should have been corrected about the tense not told it was the wrong verb. I have never heard of begreifen!
Duo is unfortunately not very smart about its corrections -- its corrections are not necessarily what a human teacher would have considered the closest correct alternative.