There are some google hits for "mylar cup" but "mylar cap" seems to be much more common.

Determination of tin in silicate rocks by energy-dispersive X-ray ...
into a Mylar cup constructed by stretching Mylar film. (0.00025 inch) over an aluminum ring using .... for each sample. Table 2 shows the compilation of all ...
doi.wiley.com/10.1002/xrs.1300180403

Mylar
... LED( light emitting diodes), phototransistor, mylar cap and resistors. ... With ultra-clear mylar film, apply it to vinyl magnet material with matte ...
www.capnito.com/Mylar.html -

diyAudio Forums Archive - SJS SE 300B with Interstage Transformer Mk2
... a nice sounding 100uF/35V Mylar Cap), so electrolytics are used. ..... I'd also throw some Common Mode Chokes plus a further of Mylar Film Caps in and ...
www.diyaudio.com/forums/showthread/t-27485.html -

Quad tweaks
... frame gently without damaging the mylar film and then store it a safe place. ... PTFE and at the same time replace the 1mfd mylar cap by a MIT PP & Tin. ...
user.tninet.se/~vhw129w/mt_audio_design/quad_tweaks.htm

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Note added at 13 mins (2007-11-30 05:47:36 GMT)
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This link might be more helpful than the others(?)

Determination of tin in silicate rocks by energy-dispersive X-ray ...
dispersive x-ray fluorescence spectrometry, Previollsly analyzed silicate rocks were treated as ... into a Mylar cup constructed by stretching Mylar film ...
doi.wiley.com/10.1002/xrs.1300180403