The whole point with a carbon tax and rebate is that it doesn’t come with all the administration and inefficiencies of picking and choosing things to subsidize and things to penalize. As soon as you start exempting this and that, you blow that out of the water.
The correct response is increasing the rebate to rural households, who statistically, rely more on oil heating, or increase the rebate across the board temporarily.
All this does is take away a very solid incentive for people who are currently looking at upgrading their home heating to chose a lower carbon option. It’s also not fair to people who recently did upgrade their heating systems, based on the expected costs.