word choice
Using the phrase “as a gesture of good will” is usually reserved for formal relationships and relationship building. It’s an emphatic supplement to the act (the act of giving, for example), for the purpose of conveying that the intent of the act is for a purpose. The purpose, of course, is to create or improve good will between the parties.
While I say it’s reserved for formal relationships, you can have instances where it is used between parties who have both a formal and informal relationship. For example, the people you work with are known to you on both levels. At some point in time, one of them may have to address your formal working relationship (maybe to renew your contract, for example). At that point, they might use the expression. But it’s in the context of the formal relationship.
You might use it informally. To mend your relationship with someone, you might say it while at that same time performing some act to improve the relationship. To do this informally is to stress how seriously you take the personal relationship.
