The graffiti is believed to have been sprayed on the building in the early hours of Tuesday morning.
The incidents happened in Rasharkin, County Antrim, on Sunday.
The ongoing closure of Kilrea Bridge is affecting trade in the County Londonderry village.
Crowds lined the streets as the annual commemoration of the Battle of the Boyne took place.
Police said graffiti was also "daubed on walls opposite" during the attack in Rasharkin, County Antrim.
Eighteen venues will host the Orange Order's annual Battle of the Boyne commemorations on Saturday.
A 58-year-old man has been sentenced for the manslaughter of another man in Rasharkin.
Police return to Rasharkin, County Antrim, following similar searches on Wednesday.
Malachy Crawford admitted punching Paul O'Boyle once, but denies he intended to kill or cause him harm.
