Pledge, which contains silicone, will not harm or otherwise damage wood or clear coats. However, it does present real problems if you ever need to have touch up repairs or refinishing done to the item. Silicone creates a very slick surface tension, which repels any product applied over it. A professional will always check for silicone contamination and will have methods for dealing with it. For example, when I have a piece that I am refinishing and I know it has been contaminated I add silicone to the new clear coat. By doing so, the surface tensions are now equal allowing the new clear coat to flow out smoothly. If I didn't add silicone the new clear coat would fish eye (looks like small craters) and I'd have to start over again. Personally, I think it is nasty stuff having no useful purpose and would love to see Pledge removed from the market.
It will also leave a blotchy appearance and when handled, will leave smudge marks. The good news for you is that the effect can be reversed by removing the silicone contamination with a wax and silicone remover wash. However, it's a powerful solvent and not something I recommend using in your home. You can have a professional do it or if you want to try it yourself, do it in an open garage with a fan drawing the air away from you. You'll also want to wear heavy duty latex gloves and be sure you're not near any open flames or anything that will spark.
Another method is to simply have the housekeeper stop applying Pledge, which I highly recommend regardless. Have them switch to Guardsman furniture polish. It is a water based product that will never build up or present any of the issues associated with most of the polishes on the market today. This method will not restore the original sheen because the silicone contamination will still be present, but with time it will help remove that melamine look.
Let me state at this point that furniture polishes are not needed, period. One of the purposes of a clear coat finish is to prevent anything from reaching the wood and a cured finish cannot be "helped" by any polishing product. In addition, there isn't a polish or any other product that will feed or moisturize the wood. In fact, you do not want to add moisture to the wood. Furniture grade lumber has a moisture content of 6 to 8 percent, which is considered dry wood. If you were to actually add moisture the solid wood or wood veneer would likely warp and crack.
The only reason to use a polish is for dusting and that can be done with a damp soft cotton cloth to remove the dust followed by a dry soft cotton cloth to remove any remaining water, which is what I do to my own furniture. If one feels they have to use a furniture polish, the only product I will recommend is Guardsman.
You may be interested to know that "lemon oil" contains zero lemon oil. It is basically mineral oil with a lemon scent added. I cannot recommend its use.