Searching for "burning house", one finds this:
Thag16.1:8.1: Having realized the supreme Dhamma,
Thag16.1:8.2: without needing anything in the whole world,
Thag16.1:8.3: one doesn’t grieve at death;
Thag16.1:8.4: for it’s like escaping from a burning house.
Although interesting as a quote, it may seem far from your question. However, if one thinks of burning little houses as an "observance", then the Buddha does indeed speak quite clearly about misapprehension of precepts and observances. It is a lower fetter.
MN64:5.10: That misapprehension of precepts and observances is reinforced in them, not eliminated: it is a lower fetter.
Consider a person who shoplifts, which is stealing. If they burn a little house every time they shoplift, is the harm done to the shopkeeper taken away? How could this burning of a little house help? That shoplifter is bound by a lower fetter.
On the other hand, consider a person who grieves for a beloved one, missing a smile or caring glance. If that person burns a little house thinking, "This grief is not mine, I am not this grief, this grief is not my self", it may help.
MN62:8.5: This should be truly seen with right understanding like this: ‘This is not mine, I am not this, this is not my self.’
Taken together, these two examples show us that we need to be careful about becoming attached to the burning of little houses, especially if we think, "the burning of little houses is mine."
Perhaps one might ask if burning the little house is escaping the burning house or clinging to it?