It certainly isn't going to help Bunter's worry about what if it turns out that Harriet wants to sack him. There he was, anxious about mere cutlery, and then this happens.

Bunter certainly provided bromide to Peter the night before the wedding, so there might have been some left. Maybe Peter thought that the aspirin, as at least ostensibly a painkiller, would be less obvious. Or was scared to look in the bag for what he might find there.