The first unaccented syllable is פִּטְ which is a closed syllable. Why then doesn't ד in the following syllable take a dagesh lene? Shouldn't the word then be פִּטְדָּֽה?
The historical elision of a vowel preceding ד could explain the absence of a dagesh qal within it. Similar phenomena are seen in words like בִּנְפֹל and מַלְכֵי. The latter probably was pronounced like malak̲e at some point, since the absolute plural form מְלָכִים has an a vowel before k̲. See, for instance, p. 40 from Greenstein's "An Introduction to the Generative Phonology of Biblical Hebrew" in "Linguistics and Biblical Hebrew" or §188.8.131.52.7 and §1.13.4 from Blau's "Phonology and Morphology of Biblical Hebrew".
The word פִּטְדָה probably comes from the Sanskrit pīta, meaning "yellow stone", according to the article "Indian Loanwords" section of the Encyclopedia of Hebrew Language and Linguistics, written by Prof. Dennis Kurzon. One may therefore conjecture that the original pronunciation of פִּטְדָה is piṭad̲a or similar.
This is sometimes known as a shewa meraḥef (שווא מרחף).