Tar sound deadening. To strip, or not to strip? Options

[Detroit]

What's everyone's take on this stuff? I'm putting a new carpet set in, so now is the time if I'm going to tackle it. Is this a must do type of job?...
It looks pretty good on the outside, but, of course, I've no idea what it looks like underneath.

[Detroit]

So, I figured I'd give everyone an update on this just in case some future member finds him/herself in a similar position.
I chose to go ahead and remove the tar deadener. Thanks again for everyone's input, incidentally.... I recall reading a thread awhile back that a forum member bought one of those oscillating cutters from Harbor Freight specifically for stripping this deadener, and as I didn't have a heat gun to try, I took a spin over to H.F. where I bought one of each. I tried the oscillating cutter first. It worked well enough that I didn't even bother with the heat gun.
Underneath I found still painted metal in perfect condition, apart from a small patch of surface rust behind the driver's seat.
The next question was how to clean up the bits of tar that didn't come up readily with the tool. I didn't have any mineral spirits or green Trader Joe's cleaner laying around, so I tried what I did have. Kerosene. That and a non scratch abrasive sponge work rather well. I've not finished yet, but here's a shot of the floors before I started with the kerosene...