We understand why people would bring their own milk to work, if the office doesn’t carry the kind they use, their own particular food, pens or anything else, but ice? Why would anyone need to bring their own ice to the office? What could be particular about their ice from home? Ice is ice.
Thus, when you put up such a ridiculous sign, you can’t expect to be taken seriously. While we also don’t understand why would anyone use this person’s ice and not the one made at the office, this is a weird sign, and those are usually answered mockingly.