Moving this discussion to the Photoshop Lightroom forum.
I already have the creative-cloud Photographer’s Bundle which includes LR Mobile so am not exactly sure how one signs up for a LR Mobile trial. Undoubtedly Adobe is hoping you like it so much that you start paying for a cloud license to keep it going.
From what you’ve said you don’t want it so I’d think you could just not pay for it and be ok, but is there some sort of nag message you get every time you start up LR or do you feel it will start changing you after 30 days or what are you asking to not happen when you say you want to resign LR Mobile?
I don’t any iOS devices so am not quibbling with your wanting not to have it I’m just wondering what the concern is after the 30 days are up.
As a Creative Cloud member (free user) you get free 30 day trial to Lightroom mobile.
If you dont want to use you can leave the Lightroom trial as it is.
If you want to delete the files if they are synced by chance follow the steps as below:
To remove all your photos from Lightroom mobile, select Delete All Data from the Lightroom mobile preference panel. This option also deletes the files that control Lightroom mobile, all metadata and collection data and removes all images from the cloud. Photos on your desktop computer aren't deleted and remain in your desktop catalog.
Source: Lightroom mobile FAQ
Let me know if you need more help on this.