iOS 9.3 Offers Update to iOS 9.3
Update (March 31, 2016): Apple has released iOS 9.3.1 (13E238***) to fix more issues. If you update to that, this issue will be resolved.



Original Answer

There were some issues in the original release of iOS 9.3 (13E233*) for older devices. A newer build (13E237**) was released on March 28, 2016.

You can check your installed build in Settings &gt; General &gt; About &gt; Version. If your installed build is 13E233*, that may be the reason for your indication. Whether you choose to update is your choice. If you choose to not, then you may have to just deal with the notifications (until the next real update).

Note: Build numbers vary per device.
13E233*: all devices except iPhone 6s/6s Plus and iPad Pro (9.7 inch).
13E234*: iPhone 6s, iPhons 6s Plus, iPad Pro (9.7 inch).
13E236**: iPad 2 (3G, GSM).
13E237**: all iPads except iPad Air 2, iPad Pro (9.7 and 12.9), iPad mini 3 and iPad mini 4. all iPhones except iPhone 6/6 Plus, iPhone 6s/6s Plus, and iPhone SE. iPod touch (5th Generation).
13E238***: all devices currently supported by Apple.