Are you in Australia? I'll answer for there anyway. You're probably in trouble. A few preventative measure existed, such as treating wood with kerosene, carbolic acid or bichloride of mercury or, in India, the caustic oil from raw cashews.

Actually getting rid of a colony was harder though. Some suggestions included brine, or fire, though that was probably more of an outdoor solution. A D. Donovan suggests introducing a colony of black ants, and the author of this piece suggests tame anteaters*. The most common method, if much less interesting than tame anteaters, seems to have been arsenic. This could either be a bait: mixed with flour and sugar, or even other termites, or it could be directly sprinkled on live individuals. The theory was that the poison would then be spread through the colony via cannibalism.

If the worst came to the worst though, rebuilding in a wood the termites didn't like could be the only option. What woods these were were believed to be varied between authors, but some mentioned included the Sugar gum, native paperbark and stringybark.

*And explains that phrenologically, on worker termites the bump of destructiveness is largely developed.

No matter what the year, finding out that termites are eating your newly constructed house is always bad news. However what makes your case in 1882 interesting is how you view and potentially try to deal with this crisis. As John Clark argues in his Bugs and the Victorians, the second half of the eighteenth century transformed the way we identify certain insects as pests, how we try to deal with these pests, and who we consider an expert in dealing with the nuisance insects.

If you're living in the the english speaking world and generally keep up with the news then you'll have read all about the threat of insect pests. France, the USA and the rest of the world suffered devastating and very well publicized insects crises in the years prior to your termite problem. France faced the existential threat of the phylloxera aphid in the 1860s and 70s, which seemed destined to wipe out wine production in France and the rest of the world. The outbreak of the Rocky Mountain locust between 1873 and 1876 threatened to unravel all the work America had done to settle the Great Plains. Then in 1877 Europe panicked at the threat of the Colorado beetle invasion. Spreading across North America at a rate of about 70 miles a year, this was a was of devastation that had decimated the potato crop. Newspaper archives in Britain are filled with intensive coverage that year of the dreaded Colorado beetle (many articles eerily echo articles published today about the threat of the Coronavirus). In the wake of these pressing insect problems, the way people saw insects changed. Whereas they had been earlier been seen as a nuisance but part of the natural order, now certain insects had become dangerous invading pests.

In the face of these insect crises pressure was on for a solution. Governments on both sides of the Atlantic enacted laws to control the import of produce, inspect incoming wares, and deal with outbreaks of insect pests. In academia we see the simultaneous emergence of the expert entomologist. The expert on insects had previously been seen as a crazed amateur (indeed entomology interest was used at least once in Britain to try to dispute a will) or as a dead end within zoology. In the face of ravenous aphids, locusts and beetles and new rank of experts asserts itself in the academic and technocratic ranks.

However, we're more interested in what you can practically do. According to Clark, the threat of the Colorado beetle ushered in the age of the industrial insecticide and the entomological expert to apply it. Natural insecticides are a well known and well used (if at times very expensive) remedy for European gardeners and farmers, with some having been used since antiquity. However a modern pest crisis demands a modern insecticide. In the late 1860s, a farmer accidentally discovered the first of the famous industrial pesticides, when after painting his shutters a pleasing green shade, he dumped the rest of the paint on infested potato pants and saw the insects die almost immediately. This new super insecticide was called after its paint name, Paris Green, and was very quickly publicized. The age of the arsenical insecticide had begun. The development of sprayer backpacks followed soon after. By the 1880s Paris Green and other similar solutions were widely available throughout the US and Canada.

So by 1882 you may very well have some serious chemical firepower with which to deal with your termite problem. While it seems unnecessarily dangerous to apply arsenic all over your house, the fact of the matter is that this was a very popular paint solution. Especially if you are living in the USA or Canada you might very well decide to deal with your issue by painting your entire house a pleasing shade of Paris Green.

Source:

JFM Clark, Bugs and the Victorians, Yale University Press 2009