There are three reasonsd it could go wrong, and all three have been mentioned already. I'll just post to confirm all this

1. Your textured background looks too much like other colours in the palette. If this happens the textured background will use colour from other palette entries (which will mess up stuff). They dont have to be TOO much different, just unique. For example, if you only used blue throughout the entire set then add a small amount of red or green into your textured background, the difference is barely visible but keeps the colours unique.

2. Use palette entries 176-209 for the textured background (the reason the above point goes wrong is because the colours aren't in these palette entries)

3. Make sute you have all 32 colours of your textured background in your tileset image. JCS will only compile colours that are inside your tileset image, dont matter if they are in your palette or not, if you didn't place them inside the image itself JCS will replace it with other standard Jazz2 colours.

Need a palette editor? Nothing is better than Palette Suite, trust me on this one. Here's the link to it, have fun
http://www.geocities.com/alister_j_t/PalSuite/Index.htm

Also, here's an image I made to try and explain all the different parts about making a textured background, good luck!
http://users.surfanytime.co.uk/disguise/texturehelp.gif