He who is Oren said on Mon, 04 Dec 2017 12:33:32 -0800:

I'll defer to the expertise of others, but if you wiggle the wire does
the "scratchy sound" increase?

Perhaps a speaker wire connection is less than satisfactory. Ground
wire on the stereo needs to be checked -- maybe?

That's a good idea to wiggle wires (I haven't done speakers in years).
The car is at college so it only comes home to do laundry.

When it comes home, the neighbor will call me and I'll be ready.

What I'll do is:
a. Try to find a test speaker of about 20 watts
b. Make a set of jumper wires to jump one side to the other
c. Wiggle the wires to see if the speaker or the radio is bad

Incidentally, after ripping out the interior in the back, the new grills
from the Toyota dealer went in easily after drilling out the old
heat-melted posts.
http://wetakepic.com/images/2017/12/04/speaker1.jpg

The dealer parts came with these round metal clips to fasten the posts:
http://wetakepic.com/images/2017/12/04/speaker10.jpg

We originally thought the noise was because the grill was destroyed:
http://wetakepic.com/images/2017/12/04/speaker3.jpg

I think the new speakers will have to come out through the top:
http://wetakepic.com/images/2017/12/04/speaker6d52eb.jpg