I need help defeating the bandits to get the village supplies back. No matter what I do, I keep dying. The pets I'm using are my three level 60 zolnixis, Lilly, Silas, and Kuro.

I checked out some of your pets, and they're all high in intelligence, but I think your team needs a bit of tweaking.

Try reading these two guides, since they're more detailed:
Creating A Battle Party 101
Guide to Pet Speccing and Gearing!
Knowing how to build a team from those guides might help better, since I'm pretty much mimicking the build in the guides.

It's good to stat one pet to be a tank, with a bunch of HP to take the attacks. With a lot of HP, it would take awhile for the pet to die, if equipped with good equipment (I see you have lvl50-60 purple and orange gear on some of your pets; it's good; you should get more if you can).
Then have two other pets to be sole damage dealers. Their attack stats (strength or intelligence) will probably be higher than 700 if you stat them just for attacking, which will do good in the long run against the bandits.

If you need anymore help, feel free to ping me. Good luck!

Yeah, this team is made to be fast killers, they work really well in everything else, just not in this specific battle for some reason. Should I go ahead and stat an entirely new team or just work with what I got?

Fast killing is good actually. o: At least for some situations moreso than others (i.e. boss battles or wave battles).

If you have another set of lvl55s-60s, and appropriate lvl55-60 armors with good rarity (such as purple and orange armor) that match the build, you can make party. Otherwise, the more cost-efficient way (assuming you have most of the equipment to begin with) is to re-stat your party.

For example, I saw Amara and Zendaya in your Tab 2 with high levels, so they might be able to make up a second party. You can use one of the pets in your original party to fill the second one that's meant for battling toughing situations.