Part Identification - Humidity Sensor Oregon Scientific BAR208HGA
The board was obviously made in Asia - China or Taiwan probably, with some pretty gnarly touch-up by someone. Did you actually get it wet?

I think it's a pretty long shot to find the specs of an unmarked unit unless you could source a spare part from the manufacturer, however there is something you can do.

Remove the sensor, clean the board with pure isopropanol (not drug store rubbing alcohol) if it got wet and allow it to dry. Then replace the sensor with various (known) capacitors and combinations of capacitors in the tens of pF and note the readings- you will quickly discover the scaling and you can figure out which, if any, is a reasonable sub. These things are not typically all that accurate, a few percent would be good. You can always trim it a bit at one point with a fixed of variable cap.