How is Lent observance reconciled with Matthew 6:16-18? Jesus says in Matthew 6:


  16 “When you fast, do not look somber as the hypocrites do, for they disfigure their faces to show others they are fasting. Truly I tell you, they have received their reward in full. 17 But when you fast, put oil on your head and wash your face, 18 so that it will not be obvious to others that you are fasting, but only to your Father, who is unseen; and your Father, who sees what is done in secret, will reward you.


In my experience, Lent observance is a very public exercise. Maybe this is just personal experience, but for everyone I know who observes Lent, they are always very forthright, not only about their observance, but about what thing they are giving up for Lent. It seems to me that, based on Jesus instruction in Matthew 6, Lent ought be a very private practice. 

Does Roman Catholicism (or anyone else observing Lent) reconcile the public nature of Lent observance with these verses?
There is nothing about Lent observance that requires it to be public.

My experience is very different from yours, and most people keep their Lent observances very private. I don't know what anyone is doing for Lent except for my immediate family (I have deduced one person's Lent observance, but even then it was something they kept as private as possible.)

I've been part of Lent in several churches, and in no case was there any encouragement to share your observances with others. I would go so far as to suggest that if the people you are with are making it public they may be doing it wrong.

(Note: None of the churches I've been involved with were Catholic, so it's possible there may be a difference in practice there. I will leave it to a Catholic here to write another answer if appropriate.)