Jaywalker, what if what the boss expects is unreasonable?
Granted, I fully understand that none of us know the industry or what is even expected in the OP's specific working relationship. But the OP posted here, and if the OP thought to simply follow the boss's lead, then she wouldnt have posted here in the first place. I think the OP is looking for advice on what is etiquettely appropriate in a business situation. And since there were no details posted about the company, industry or culture they are operating in, then we only have the broadest information to go on, and can only give the broadest advice based on what we feel is reasonable from our experiences. Maybe the OP is young, and cleaning up would only reinforce to her boss and the client that she is subservient, or doesnt know how to act in a business setting, as another poster suggested, and thus hurt her business relationships in some way? Maybe she is expected to clean up, like you suggested? Basically, we dont know what is expected of her from her boss - but it might not even matter, because what he expects, might not be appropriate either, and it might be a boundary-setting opportunity for the OP.
So in reality, it is valuable for both of us to post, as well as our reasons why, so that the OP has multiple opinions to consider and decide what is applicable to her situation. I wouldnt just 'take a cue' from my boss for the very reason mentioned above - I would also exercise my own judgement, and if I didnt have it, I would ask others so that I was well informed before the situation took place. It sounds to me like this is what the OP is doing.