If you follow those leads away from the battery and into the unit, you'll see that they are connected to a black or white plug/terminal. that is a quick release, so you can grab hold of that and wiggle it loose away from the unit, and it will come right out.
That sometimes is not enough to make the alarm go away. You sometimes have to disconnect the battery alarm jumper, but that is located in the other box, the ONT. When you open that, they are labeled. you find the right one and disconnect it.
If you don't feel comfortable doing it, you have a couple options.
If you have had service less than a year, then Verizon will replace the batter for free.
If you have Verizon's Expert Care service then that battery is free for the life of your expert care subscription.
If you have had service over a year, then you have to make yourself a value judgement. If disconnecting the Jumper is easy for you, then go for it, otherwise if it's not, then go to amazon.com and search for a 12v 7ah sealed lead acid battery. It's about 12 bucks.
