Gov. Charlie Baker returned the Legislature’s bill to tax and regulate short-term rentals on Wednesday, waiting until the day after the House and Senate adjourned formal sessions for the year to propose an amendment that would exempt homeowners that rent out their units for fewer than 14 days a year.

The governor is also proposing to limit the amount of information that will be made available through a new public registry of short-term rental housing units, and said changes to the definition of a short-term rental must be made in order not to violate the terms of the bonds used to finance the Boston Convention and Exhibition Center’s construction.

The governor’s amendment could imperil the compromise struck between the House and Senate, but should not come as a surprise to lawmakers.

House and Senate leaders, who sent the bill to Baker on Monday, were briefed on some if not all of the governor’s concerns Monday night, and the News Service reported then that Baker’s team was considering an amendment to exempt units rented for less than 14 days.

According to a senior administration official, the governor offered at that time to return the bill before the end of formal sessions if House and Senate leaders would agree to the changes. They did not.

The amendment filed by Baker would allow property owners that casually rent their houses or apartments for two weeks or less to avoid having to collect the state’s 5.7 percent per night lodging tax from guests, register with the state or obtain $1 million liability insurance policy on their property.

The 14 days threshold is significantly smaller than the 150 days Baker proposed in his own bill, but would address the governor’s concern that people renting their houses through Airbnb for a few days to generate some income not be treated like professional property owners operating de facto hotels.

The administration estimates that the change would reduce the state’s projected new revenues of $25 million by $300,000 and exempt about one-sixth of operators who would otherwise be required to register and collect and remit taxes.

The House and Senate will now have to determine whether they can address the governor’s amendment – either adopt it, reject it and return to him the original bill, or propose a third way – in informal session when an objection for any one lawmakers can halt action.

In the House, 30 members voted against the compromise and in the Senate there were eight no votes.