How should I ground a heat pump capacitor?
The metal strap that holds the cap in place is the ground. You have 3 connections so that is a dual element cap it has 2 capacitors internally normal values are like 5uf &amp; 45uf  370-400v . 
1 terminal will be common “C” and normally one will have a “S” start and the other “R” run , with a metal can the case is grounded by the strap on every system I have worked on.
Note the strap for your cap is just to the left in the photo.
I did remember some caps are labeled “c”  common and “H” for the compressor “f” fan this is where a dual element cap is used for starting 2 different motors but they can be used interchangeably if the ratings are the same the 45uf element is for starting the compressor and the 5uf element is for the fan or in some cases the run of the compressor.