If you do not wish to include D at any point, you can simply not include it in the design generation. But, I don't think that's your intent, correct? Assuming that you do wish to include all your attributes, and for each set have a different attribute held constant (and invisible), what is going to happen after designing your experiment using DOE > Consumer Studies > Choice, is you will get a table of your choice sets, which one of the pair in each row. If you indicate you want only three attributes to vary in a set, at least one of the attributes will be fixed. There isn't a way to suppress the display of the fixed attribute for each choice set (and, it will be a different attribute in each choice set that is held constant). But, I expect you won't have people using JMP to fill out their responses (assuming this is for human participants). So, my question was what software (survey or otherwise) will you be using? I ask because you will need to convey the survey design over to that format, and it's in that translation that you will have control over not including the details of the attribute that is constant. In the most low-tech version of this, you simply do not include the details about the attribute that is held constant when you type in the details of the choice set. Again, it's not a feature of the design, but of the administration.
That all said, your choice to not include that information is not neutral psychometrically. The absence of that attribute will certainly divert additional attention on the remaining attributes (which might be your intention), but if the omitted attribute has interactions with the other attributes you are robbing yourself of data in which that effect can emerge. You are additionally removing data for your model to estimate the average inertia of the levels of that attribute (at least when you have a no-choice option, perhaps less so with a full forced choice design). I can't speak completely to the statistical implications of that (I haven't done the necessary research to state anything definitive), but if you pursue this I would suggest finding someone expert in choice designs (which unfortunately isn't me) to think through in detail the consequences of this with you.