Once it's removed, just go into the App Store, search "Notes" and select the download icon. After that, use the device for some time and see if the Notes app is continuing to use the battery when you're not actively using it. In Settings > Battery, you can tap on each of the blue bars in the Activity graph to see what used the battery each hour.
The Battery Usage section features a chart and a table. The Usage History section, shown in Figure F, shows the history of system usage on both AC and battery power. In the first column, you’ll find a usage period–typically seven days, which may or may not be consecutive set of days, depending on how often you use your system.
Tap a bar to see activity and usage by app during that hour or day. To see how long each app was in use on screen or in the background, tap Show Activity. Battery usage is unique to each app. Graphically intensive apps, like apps that stream video from the internet and games, can use a lot of battery.
In Settings > Battery, you can tap on each of the blue bars in the Activity graph to see what used the battery each hour. Check those to see if Notes used any battery during hours which you didn't use the app. About the battery usage on your iPhone, iPad, and iPod touch
To see an overview of your battery level and activity for the last 24 hours and up to the last 10 days, go to Settings > Battery. The bars in the Activity chart show how many minutes you've used your device during that hour or day. Dark blue indicates onscreen usage, and light blue indicates idle or screen-off usage.
Battery usage is unique to each app. Graphically intensive apps, like apps that stream video from the internet and games, can use a lot of battery. Under each app, you might see these usage types: Background Activity: Most of the app's battery usage — such as playing music or tracking location — happened while the app was active in the background.