This is something you could use. Muffle strip or muffler strip is used for sound-insulating race helmets or in music engineering. But something with muffle/muffler would get you close to what "fluister" is supposed to convey.

Here an example of a sound muffler:

"Typical residential suite features

- Two-leaf panel main door with wide-angle door scope and service door with peephole
- Distilled water from special faucet Centralized water heater for each residential suite
- Pre-installed, split-type air-conditioning for living and dining areas and terminal units for all bedrooms
- All master's bedrooms with ergonomically organized lighted walk-in closet Standard organized closet in all bedrooms
- Sound mufflers for all cabinet doors

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