It looks normal here. It might be a rendering problem in your software. Did the glyph look equally strange at other sizes and in other applications?

The capital H looks strange only in the Light Display weight, set at any size, and in different applications (Indesign, Photoshop, Text Edit). I wonder if anybody else who owns the font could test it.

The capital H of GaramondPremrPro-LtDisp.otf,
release 2.000;ADBE;GaramondPremrPro-LtDisp
with internal date 21.07.2007 is definitely defective:

http://www.sanskritweb.net/temporary/GaramondPremrPro-LtDisp-H.jpg

It is strange, but the older release
1.014;ADBE;GaramondPremrPro-LtDisp
with the internal date 28.04.2005 did not
have this defect.

Who knows other releases?

....

Confirm 2.000;ADBE;GaramondPremrPro-LtDisp (character H) IS DEFECTIVE...
But newest release 2.061 is fine...