Go to icloud.com (if you have not) and make certain the information is not there. Reminders will be in the Calendar app.
If it is not there: Turn off the Reminders and Contacts options in iCloud. Choose to KEEP your data. Visit each app, just to force it to do whatever it does. Now go back to iCloud settings and turn them back on.
You need an internet connection when doing this.
If that does not work, try the more drastic measure of signing out, then back in to your iCloud account in iCloud settings. Again, because your data is not in icloud.com, choose to keep the data.
Also, if you have any apps using the Documents and Data option, it would be a good idea to either turn the feature off (temporarily (and keep)) or save the documents to some other platform; dropbox, the computer, etc. Just in case iCloud gets confused about which ones are new, or not, when you sign back in.