Is there a hypothetical unit of time that measures time backwards?

Yes. It's that little red cube of jelly like substance that Dr Who keeps in his left jacket pocket.

Congress has a corner on that market. They use it over and over again.

Yes. It's called "-t". Same unit as regular time, only with the opposite sign.

Are you pulling my leg ( )or is this an academically recognized unit of measurement?

.tekcop tekcaj tfel sih ni speek ohW rD taht ecnatsbus ekil yllej fo ebuc der elttil taht s'tI .seY

we have one in geology. Im not sure its got any use for the general public since its an inverse function based upon stratigraphy and magntic susceptibility.
We measure geologic epochs and smaller divisions in "Chrons"
When stratigraphic columns are produced , an effort to correlate these units worldwide is based upon the "chron" { time from present}.

Secondly In isotope chronology we use a value of "A" (loosely, an annum) which is a constant unit of seconds that we see in an average year. This defeats the assertion that Isotope "Time" is speeding up or slowing down) {Of course the actual second may be but who gives a ****, were all riding the same wave}.
All these chrons and anna are presented as n/A or n/C
where n = the time interval from its end to its base.

BUT, most often, when we are all likkered up, we usually say "its so many years old"
we only use the actual A's and C's in papers. (Nobody talks like that)