Holy Trinity is the local church in Georgetown with Damien Karras and Father Joseph as the the priests appointed by the church. The statue of Mother Mary was also vandalized during the events of the possession of Regan MacNeil, indicating that an innocent is being tortured by an unclean spirit.
The movie does not even attempt to answer the question regarding the desecration, and it is barely mentioned afterwards (only twice in one conversation between Karras and Kinderman, and then mostly to invoke the possibility of satanic elements in the death of Dennings). In the novel, however, Lt. Kinderman (Lee J. Cobb) scratched off some of the paint from one of Regan's sculptures and compared it with the same paint used in the church desecrations. It matched, implying that, in Regan's possessed state, she was the one vandalizing the church. This was made more certain when he found that the blasphemous Latin altar card was typed on the MacNeil typewriter.