I suggest that the team **identifies with** the quality of its output.

>[Longman](https://www.ldoceonline.com/dictionary/identify-with)  
identify with: phrasal verb  
1 identify with somebody/something to feel sympathy with someone or be able to share their feelings  
*Humans can easily identify with the emotional expressions of chimpanzees.  
He identified with our distress.*  
2 identify somebody with something to think that someone is very closely related to or involved with something such as a political group  
*She has always been identified with the radical left.*  
3 identify something with somebody/something to think that something is the same as, or closely related to, something else  
*the attempt to identify crime with poverty and social problems*

The Longman examples show how the subject associates themselves - or is associated - with the object. This is appropriate for your team, which associates itself closely with quality. There is no suggestion of hubris or arrogance in this usage, which merely asserts an association without any judgmental overtones.

If you need to communicate the commitment to quality and to focus on the team's actions while not boasting, and having the humility to admit that they may be flawed, you might also write:

*our team **strives** for quality of our output*

or 

*our team **aspires** to quality in our output*

>[Merriam Webster](https://www.merriam-webster.com/dictionary/strive)  
*strive*, intransitive verb  
to devote serious effort or energy : Endeavour  
*strive to finish a project*

>[Cambridge](https://dictionary.cambridge.org/dictionary/english/aspire)  
*aspire*, intransitive verb  
to want something very much or hope to achieve something or be successful