The first time each day you meet your housemate or colleague, you say hello, good morning, etc. The second time, passing in the hallway, you push your lips together--not a real smile, not a grimace, not a mouthed word, just an acknowledgement. What is the word for this silent, minimal exchange upon repeated interaction?
Non Verbal Acknowledgement
The context is different in the source I cite here, but you can equally well apply the term to your hallway acknowledgement of your friend, as well as acknowledgement that you are listening to a teacher in a classroom, as in the following example:
Acknowledge other people's contributions by...nodding your head. Speakers find such signals reassuring as they show their ideas are being listened to and valued...
If you were specifically greeting your friend without talking, (and not for instance just acknowledging them in passing after you have already met that day) then:
Non verbal greeting
Would also work and be more specific.
They exchanged looks.
exchange looks -
PHRASE to look at someone at the same time as they look at you, especially to communicate something — macmillandictionary
Also quoting an answer (with my highlighting in bold) at https://www.italki.com/question/227763 :
Generally, two individuals have to "look at each other" in order to "exchange looks."
"To look at each other" is a neutral statement of act. When A looks at B, and B looks at B, they are looking at each other (お互いを見る）. "To exchange looks" goes a step further. In addition to physically looking at each other, when A and B exchange looks, it is implied that they are communicating some common understanding/knowledge/agreement by the looks on their face without expressing their thoughts out loud.
For example, A and B both know that C is a very boastful person. When C predictably starts to tell tall tales about how smart he is, A and B may "exchange (knowing) looks," acknowledging, for example, their common dislike of C through their facial expressions, without saying anything verbally.
For a noun, you could say they had an exchange of looks but that's sounds a bit wordy to me.
Your question was regarding "when you push your lips together." The simplest description I could get it down to was the expression "purse" your lips together. This usually has negative connotations, so if you were to use the expression in a positive, communicative way, one might say something like: "As we passed each other in the hall daily, my colleague and I politely pursed our lips in silent acknowledgement of each other as the workday dragged on." If there is no hint of a smile, then it's difficult to put this non verbal communication into proper context without more information, but I hope this helps.