I would tear the paneling down depending on how cheap it is it may be made of pressed wood which would not hold the tile or grout and also likely to buckle out on you so hard to say without seeing it but if you are going to do it my mottos is do it right the first time.
Tile over wood paneling.
It will ensure that the tile sticks the way that it should for as long as you need it to.
Hardibacker is the most important part of the entire job.
A regular non modified thinset mortar will fail to stick to the wood paneling so if you are planning to tile directly over a wood panel this is one of the few adhesives that will allow you to do so within tile installation guidelines.
Step 3 test fit each piece of tile over the backer board and cut all necessary pieces to size with a tile saw.
Hgtv star chip wade shows you how to modernize old school wood paneling with paint for more follow the hashtag rachaelrayshow.
For wall installations plywood is overkill beneath the concrete or fiber board which is designed in five eighths inch material for wall settings.
If possible you should always use concrete board underlayments rather than plywood.
The raised pattern and texture makes it a great cover up for old wood paneling.
You will simply need to screw the hardibacker to the wood paneling.
While often times it is said that you should not try tiling over wood paneling there are many ways to avoid typical problems associated with doing so either by using membranes or altering the tile size and weight.
The preferred method for tile installations is to use a sheet of underlayment.
If you are installing any type of tile onto the face of wood paneling for a backsplash you can use mastic to install the tile.
Place the backer board over the paneling and then secure it to the studs in the wall with drywall screws and a screwdriver.
Make sure that you use screws that are long enough to go through the hardibacker and into your wood paneling.
After the wall.
Things needed gloves protective face mask tape measure 1 2 inch tile backer board hardibacker carbide tipped scoring knife chalk line tiles thin set tile mortar 1 4 inch notched trowel tile spacers rubber mallet beating block tile grout sponge tile sealant.