Luxembourg was invaded on Hitler's orders in 1940 and remained under German occupation until 1944. During this period it was illegal to fly the Luxembourg flag or celebrate any national symbols, and the country was essentially absorbed into Germany.

Luxembourg was viewed to have a historically supportive relationship with Germany, through economic agreements, treaties, and collaborative actions. This was used as evidence that it should become fully German by those who were tasked with the justification of occupation. It was also viewed as tactically valuable, given its location and proximity to other German war aims.

In my half an hour I spent on this I didn't find any direct quotes from Hitler on the subject of Luxembourg. If I had more time I would keep looking as I'm sure it's out there. Hope this helped a bit though.

Sources: Pit Peporte, Sonja Kmec, Benoit Majerus and Michel Margue. Inventing Luxembourg: Representations of the Past, Space and Language from the Nineteenth to the Twenty-First Century. Leiden, The Netherlands: Koninklijke Brill NV, 2010.