Two things, and neither of them happens on its own.
Clearing the filter row now keeps a snapshot, and the same spot turns into an
undo arrow that puts it back. Taking the filter apart chip by chip does not
leave one, because that is someone changing their mind rather than setting
something aside.
A filter can also be saved under a name and picked again later, per person and
per board.
Nothing is restored automatically when a board opens, which is the whole
reason this may live in localStorage at all. Two windows on the same board
would otherwise pull one stored filter back and forth. The storage is read in
three places and only one of them dispatches, inside a click handler.
The keys and the payload are Pro's, so saved filters carry over to an upgrade
instead of being left behind. Community's own filter dimensions ride along as
extra fields that Pro reads as absent.