All that can presently (April 2022) be gleaned about
Margaret Mudge from sheet music covers and by Internet searching is that
she was presumably an American actress/dancer who has been featured, together with her partners Leon van Dell and Sheriden Du Pont, on 2 works published between 1913 and 1914.
The sheet music cover
California Sunshine (1913) music by
Harry Jentes, and published by
Theron C. Bennett Co., New York, USA notes that she was
Late of the London Opera House, London and The Cicel, Paris.
Surfers are welcome to contribute any further information about this performer.