We coat by dipping the board during manufacturing - which gives the prettiest finish.
Although the varnish does impede re-work - it is quite possible to re-work the board and desolder joints as necessary without first removing the varnish, which melts and moves aside under soldering temperatures. Be warned that the melted varnish does tend to clog up desoldering tools.
If you really do need to remove the varnish - it is soluble in acetone, which is readily available and somewhat cheaper than the special thinners sold for use with the varnish.
If it is required to re-varnish the board after re-working you can apply the varnish to the affected area with a small brush - though you will never get the same finish as achieved by dipping!
In most cases however it really is not necessary to re-varnish the reworked area.