It seems that they may not be so responsible as some think for the spread of the paralysis tick (if that is the tick you are referring to) as they don't roam very far, and as such are less likely to be the carriers of the tick.
Here's some of the text from the above link.
"Living with bandicoots
Bandicoots are protected in NSW, and it is illegal to trap or kill them without a licence. You can contribute to the conservation of bandicoots and other native species by keeping your pets locked up at night, and by not allowing your pets to enter national parks at any time. The scent left by cats and dogs in bushland areas may discourage native animals from going about their natural activities.
Native animals such as bandicoots may treat your garden as a sanctuary from time to time, and you can live in harmony with them by accommodating them in purpose-designed areas. You can establish a separate area in the garden, away from the places that are used most by your family and pets, which provides native birds and animals with shelter and food. You can then use a more formal, manicured area for entertaining and relaxing.
Alternatively, you can keep bandicoots out of your backyard by building bandicoot-proof fencing. Use fine galvanised wire mesh, or any other material with gaps no larger than 20 mm. The foot of the mesh should be buried to a depth of at least 150 mm, and the fence should rise at least 500 mm above the ground. Bandicoots and ticks
A wide range of native and introduced animals are hosts for the paralysis tick, which can also afflict humans. Highly mobile animals, such as foxes, dogs, and domestic and feral cats, are particularly susceptible to picking up ticks as they wander long distances through bushland areas and backyards.
Bandicoots also act as hosts for the paralysis tick. However, they tend to roam over a comparatively small range, often staying within half a hectare of their nests. As a result, they are less exposed to the risk of ticks. Although some people associate bandicoots with ticks, this may be because humans tend to pick up ticks most easily in long grass or thick scrub - which also happens to be the type of habitat favoured by bandicoots.
You can help to reduce the spread of ticks in your area by:
*Regularly maintaining your garden to control tall grass and weeds, particularly the noxious weed lantana. *Spraying yard areas with a malathion-based spray, which lasts for about two days. A natural alternative to chemical sprays is a mixture of chilli (cayenne pepper), garlic and vinegar. After being left to brew for a few days, the mixture will discourage most pests if sprayed around the garden. However, remember that any such treatment will also harm beneficial garden invertebrates. *Regularly grooming and inspecting pets."
