This is a CSS problem.
I suggest you learn how to inspect the DOM and CSS on your device. It looks like this is on iPhone and you are using something like PhoneGap/Cordova but in any case you are using a UIWebView or WkWebview.
You can connect a USB cable to a Mac and debug/inspect using desktop Safari. (For Android, you use Chrome). You will have to find out how to enable webview inspection in your development platform.
You are unlikely to get any more than general answers here. jQuery Mobile is outdated, unsupported, hasn't been updated for the latest browsers and devices, and likely never will be. Even those of us who answer questions here haven't used it in a project in several years. We (OK, can't answer for others, but I can for myself...) are answering from the viewpoint of a fading memory of an abandoned library.
Your platform (PhoneGap/Cordova? Something else?) will have some specific documentation on using inspection tools.
Once you can inspect/debug CSS, you can examine the document to see where your "lines" come from, figure out how to alter the color, etc. (You can interactively change the CSS and see the result immediately!)
This is a useful tool to learn, regardless of whether you are using jQuery Mobile or any other library or CSS framework.
I can't guess why it changes when you tap. You've given too little information to guess at it.
One possibility for the lines is that you've set a fixed height and it is off by one (or a small number) of pixels.
