The measure will see all passengers arriving by boat, train or plane take a Covid-19 test before departure.
A committee is calling for views as it examines the Scottish Parliament's procedures over the last seven months.
The Scottish Government says taxing the new £500 payment could mean fewer people apply.
Call comes from Scottish Lib Dem leader Willie Rennie amid conflicting statements from ministers.
A total of 11 people have now died with Covid-19 at Redmill Care Home in West Lothian.
There are 435 new cases in Greater Glasgow and Clyde, 346 in Lanarkshire and 114 in Lothian.
Nicola Sturgeon urged Scots not to visit other people's homes or travel south to watch Saturday's Old Firm clash.
Scotland Yard says MP will face no further action over 800-mile trip she took after testing positive for Covid.
Measures banning household visits and limiting other gatherings to six people will stay in force.
The First Minister defended the latest restrictions as 'tough but necessary' in the fight against Covid.
Tuesday's figure of 1297 infections is the highest daily total in Scotland on record.
Number of outdoor visitors permitted extended while indoor visits of up to four hours will be allowed.
However the First Minister urged Scots living in hotspot areas to avoid unnecessary travel due to new coronavirus restrictions.
There are 961 new cases of coronavirus in Scotland but no deaths reported in the last 24 hours.
It takes the death toll among confirmed Covid-19 patients to 2538.
Strict new measures will come into effect on Friday for pubs, restaurants and cafes across Scotland.
Licensed premises in five health board areas to shut, and the rest of pubs in Scotland hit with 6pm indoor curfew.
The 775 new cases amount to 12.6% of newly-tested Scots, among the highest percentages recorded.
Margaret Ferrier had already travelled by train to Westminster even though she had developed Covid symptoms.
But the Portuguese islands of the Azores and Madeira are now exempt from 14-day quarantine for travellers.
