The lipid membrane is a principal building block in biology, technology and industry, where it often occurs supported by other hydrophilic structures. Interactions with the support can affect the physical behavior of the membrane from the local organization and diffusion of lipids and proteins, to phase transitions, and the local mechanical properties. In this study we show that supporting substrates textured with nanoscale hydrophilic and hydrophobic domains can modify the membrane's chemical composition by selectively extracting cholesterol molecules without affecting the remaining phospholipids. Using polydimethylsiloxane (PDMS) substrates with various degrees of plasma oxidation, we are able to trigger dramatic changes in the membrane morphology and biophysical properties, and relate them to the amount of extracted cholesterol. We also show that it is possible to control the cholesterol extraction through mechanical extension of the flexible PDMS support. Given the ubiquity of bio-substrates with textured surface properties and the wide use of PDMS we expect that our results will have implications not only in biological and chemical sciences but also in nanotechnologies such as organ on a chip technologies, biosensors, and stretchable bio-electronics.