Her main subject area is looted art; a number of museum holdings and large Jewish collections have been processed by her.

Since 2003, Terlau has worked as a freelance art historian with provenance research and consultations for museums, foundations, private collections and the media.

[7] For the heirs of the art dealer Jacques Goudstikker, who had to flee Germany as a Jew in 1940, she and Clemens Toussaint's team located numerous objects in the collection and achieved their partial return.

[7] In 2017, the Kunstmuseum Gelsenkirchen [de] and the Museum Folkwang in Essen commissioned Terlau to investigate the acquisitions via the Hermann and Aenne Abels galleries from the period between 1933 and 1968.

In 2019, the two researchers determined, among other things, the legality of the transfer of ownership of four Piet Mondrian paintings in the Kunstmuseen Krefel [de].