Converting the per square foot price to the per square metre price is a simple calculation, and to be able to do this you need to know the conversion factor from square feet to square metres.
one square foot (ft²) = 0.09290304 square metres (m²)
You received a quote of $5.63 for work that needs to be done per square foot basis, but your plan is in metric, so you need to know what it is in square metres to make sense of it.
5.63 ÷ 0.0929 = 60.60 The per square metre cost is $60.60