The real issue with your idea is that in many ways it is not entirely debatable. For the Teutonic Knights, as for the other military religious orders - the Templars and Hospitallers in particular - it is generally argued that their primary motivations changed at some point.
To create an analytical thesis statement from this topic, you might consider whether there is a point in time (or a short span of time) when the motivations of the Teutonic Knights began to change. To say this, you can indicate that over a certain period of time, the Teutonic Knights began to cite not religious devotion/duty but secular concerns as their reasons for crusading to the Holy Land.
You can also argue that religious convictions was never really the primary motivation for the Teutonic Knights going on crusade. You could say that contrary to the commonly-held perception among medieval scholars, the Teutonic Knights gave more weight to their secular interests than to their religious convictions when they crusaded to the Holy Land.
You can also argue that one particular event demonstrated a transition to more secular concerns. Depending on how specific you need to be for your essay, you can indicate that a particular event marks (or is evidence of) the change in their motivation.
Ultimately, what will make your thesis more analytical is a particular approach to your topic. Being as specific as possible is key to achieving this. Rather than talking in broad terms (unless your writing project is expansive), focus on individual parts of it. Since you seem to want to argue from a development over time, you should emphasize particular points in time (specific period or event) or particular aspects of your statement (the more secular means, for example) to narrow your focus. The nature of your evidence will determine which approach will be the most effective.