We just moved and brought along our Samsung TV. We had to switch to
Time Warner and they suggested a back up battery for our new telephones.

In big letters: Caution don't transport if damaged... etc. LITHIUM BATTERY

Well I've seen all kinds of serious problems with these batteries. How can I
Avoid using a lithium battery. There must be one in my phone right now.
My TV is a Samsung and they may have one too. I'm pretty nervous about
All of this. Any advice?

Not to be a "Smart a***", but is the battery in question damaged in any way?

I haven't opened the box... but the box is not crushed

Okay, I guess I don't fully understand your question. If the battery is packaged properly there is no danger in transporting it anywhere.

You can't avoid using a Lithium battery, that is what the unit is designed for.
Those are very small batteries, probably not subject to spontaneous combustion.

Why do you think your TV has a lithium battery?

I threw you off by saying I brought my Samsung TV... the battery is for the phone

It's the word "probably" that scares. Turns out there are thousands upon
Thousands explosions... recently one woman with headphones on an
Airplane exploded in her ear... spontaneous combustion of wireless
Devices... I just wish there was something I could do... like change
Batteries and use another companies...

I think you are overreacting! " thousand upon thousands"? Anecdotal evidence? Cell phone batteries are quite different than home phone batteries. Cell phone batteries have to hold a lot of power and are charged differently. Do you have a cell phone? If so, are you worried about that battery?

No I don't have a cell phone... well I have a flip phone (yes, I'm a very
Senior person) The battery is for the new phone AT&T phone, Time Warner
Service

A flip phone is a cell phone, I have one too, BTW I'm 75. A flip phone has a Lithium battery too.

I have used this battery in my phone backup for years and years. There aren't any problems. You are over thinking it. You TV has batteries inside also but are safe. You can actually have them replaced if your TV goes down. They are not a problem either

Really? I've decided to get an Iphone 6S (Consumer Cellular)