Humidify means to supply water vapor beyond room conditions.  This is
commonly used to soften the paint, or the support (canvas), before
removing planer deformations (concave or convex areas) in the
paint/canvas layer.  Support can be used as either a verb or noun: (n)
support is the canvas; (v) provide support when the paint/canvas is
softened by the introduction of humidity.   Verso is a book term, it
means reverse; this is (unfortunately) common usage in conservation.

If a painting is face-up on a working strainer, then the reverse would
have to be supported during humidification because it will soften and
sag while depth of the wooden members (1- 2") prevent it from resting on
a table surface.  Usually, a painting is face-down on a working
strainer.  There are reasons for the opposite, however.  My GUESS is
that they intend to remove planer deformations while the painting is on
a working strainer by humidifying, while supporting the reverse, and
then flattening under weights, or on a vacuum hot table.

Of course, many assumptions have been made to give a quick answer.  The
actual meaning of the "phrase" is to be found in the context of the full
report and bid. I hope the definitions and guess help.

Timothy Vitale
Paper and Photograph Conservator
and Consultant