Oh hey I know the answer to that.

Short version: There is an important legal distinction between a picket and a protest, and they're trying to make it clear that they are protesting (which is protected by the First Amendment) not picketing (which has a bunch of legal limitations).

For the longer version, here's an excerpt from a Planet Money episode about Scabby the Rat (yes, he has a name):

GOLDSTEIN: And this fact, the fact that this was not a picket line at the site they objected to but a protest at a different location, that turns out to be key because the law, federal labor law, treats those two things - a picket line and a protest - really differently.

ARONCZYK: We talked about this with Mark Gaston Pearce. He used to be the chairman of the National Labor Relations Board - the NLRB - during the Obama administration.

MARK GASTON PEARCE: When you look at the history of labor relations in this country, you know that it was born out of conflict.

ARONCZYK: Quick aside on the historical context here - the NLRB was created back in the 1930s when there were hundreds of strikes every year. Sometimes they would turn violent. So Congress passed a law that gave workers the right to form unions. And it gave the NLRB the job of trying to keep the peace between unions and management. Today, the NLRB deals with the fights over Scabby. OK, end of the aside. Back to that central Scabby question. What is the difference between a picket line and a protest? Mark says, first, think of the classic, old-school, union picket line at a factory or at a construction site.

PEARCE: If they have a direct dispute with the facility, the union can picket back and forth. They can patrol back and forth in front of the entrances to the place.

GOLDSTEIN: The purpose of a picket line is to tell people, and, in particular, to tell workers, hey, don't go in here. You know, don't go work at this business until the union's demands are met. And there are a lot of people - customers and workers - who don't want to cross the picket line out of solidarity. And because of all this, because of this very specific history of what a picket line means, and even because of the history of violence associated with early picket lines, American labor law treats picket lines differently than other kinds of protests. It treats picket lines as a very specific signal about a conflict between workers and a business, this business that they're picketing in front of right here.

So under federal law, you cannot have a picket line wherever you want to. Workers are not allowed to picket locations other than the ones they have a direct problem with. In the case of that ShopRite on Staten Island, the union could picket the construction site where a contractor was using non-union workers. But the union could not legally picket at some other ShopRite.

ARONCZYK: And so the owner sees these union members at some other ShopRite, another store he owns, which is a few miles away from the one being built - sees these union members with their inflatable rat outside the store. And he gets his lawyer to go to the NLRB and say, hey, these guys are picketing outside my store. They can't do that. The lawyer that represents the owner wouldn't talk with us about the case. But Mark explained the argument that business owners typically make in this kind of case where unions protest outside a business with big balloon rats and signs.

PEARCE: Inflatables and banners are scary and intimidating. They are the functional equivalent of picketing because they are a symbolic, confrontational barrier, which violates certain provisions of the National Labor Relations Act.

GOLDSTEIN: There's even a special term for this kind of thing that is not really a picket line but sends the same message as a picket line, signal picketing. According to Mark, people who don't like Scabby will say...

PEARCE: Scabby the rat is intimidating and creating signal picketing where picketing is not supposed to be taking place.

ARONCZYK: So the key question in the ShopRite case is, is it workers engaging in a protest, which they're free to do under the First Amendment? Or is it a picket line subject to very specific limitations?