Is it at all possible to get info on the size (sq. ft) of the current filter? How often did the previous owner need to backwash and recharge?
The point is, pools are very often built with undersized filters. So the current filter may not be correctly (as we at TFP define it) sized for your pool. What I would hate to see the warranty company do is put on a filter that is not sized right and then you have a great, brand new DE filter that you have to constantly backwash to keep the pressure in check.
DE filters have the finest grade of filtration (3-6micron particle size) because the filter mesh is impregnanted with diatomaceous earth. So, when you backwash a DE filter, you essentially flush out approximately half the DE in it and that has to be recharged each time you backwash. 25lbs of DE costs roughly $36. Depending on the size of the filter you may use 4-6lbs of DE with every backwash. So if your filter is undersized, then the pressure will rise frequently and you'll be using a lot of DE.
Cartridge filters are just big filter bodies with one or more cartridges in them. There's no backwashing involved as you simply disassemble the filter when the pressure rises and wash the cartridge off with a garden hose. Cartridge filters are usually good for ~ 10-15micron particle size.
Sand requires backwashing but there's no recharging of the media, just backwash, clean and go. Sand filters don't do much better than 30micron particle size. You can add small amounts of DE to a sand filter to improve filtration performance but you must recharge the DE with every backwash.
Before you sign off on the warranties company's proposed fix, please post the details here and we can help you sort it out if it's a good deal or not. Some warranty companies will offer the option of just paying you in cash if you don't like what they offer so you may be able to get some cash from the warranty company and add in some of your own to get the best filter option for your pool. Though if you don't take their offer, you may have to do the installation and PVC plumbing work yourself.