In phonetics, I find three terms used to designate a silent letter (or letters):
'zero sound', or simply 'zero'.
Of these, 'silent letter' (1) appears to be most common. The uses, however, might be said to be colloquial, rather than technical and specific to phonetics.
'Mute letter' (2) is also used. The term is attested in use with a special sense for grammar and phonetics, as shown in OED Online:
mute, adj. and n.
4. Grammar and Phonetics
b. Of a letter: not pronounced, silent.
["mute, adj. and n.3". OED Online. June 2016. Oxford University Press. http://www.oed.com/view/Entry/124309 (accessed July 18, 2016).]
Attestation ranges from 1638-2005. The publications cited are not, however, exclusively devoted to phonetics, but are more general: Barnabæ Itinerarium (1638); Hist. Druids (a1722); Proc. Philol. Soc. (1840); Dict. Mod. Eng. Usage (1926); Understanding French Verse (2005).
This sense of 'mute' is invariably adjectival.
Other—but obsolete, historical and rare—senses of 'mute' used as a noun and adjective in phonetics are given. These obsolete senses do not offer an answer to the question, because even if they were not obsolete, etc., they refer only to 'silent' consonants:
4. Grammar and Phonetics.
†a. Of a consonant: plosive, stopped. Obs.
†c. Of a consonant: voiceless. Obs.
1. Phonetics. A mute or stopped consonant; a plosive. Now hist. and rare.
'Zero sound' (3), also 'zero', however, promises to offer a complete and direct answer to the question. The term and the (absence of) sound it denotes is represented in IPA with ∅.
In an alphabetic writing system, a silent letter is a letter that, in a particular word, does not correspond to any sound in the word's pronunciation. Phonetic transcriptions that better depict pronunciation and which note changes due to grammar and proximity of other words require a symbol to show that the letter is mute. Handwritten notes use a circle with a line through it and the sound is called "zero"....
(Wikipedia, "Silent letter")
While I was at first incredulous (for philosophical reasons, among others), I quickly uncovered support, that is, attestation for the sense, in a wide range of publications specifically dealing with phonetics. I offer a somewhat random selection from those publications:
In accordance with the phonetic laws of the Türkic language the word aluank could have variants Alan, Alban, Alvan. The sound k, apparently, is a part of an affix of belonging -nyky (Aluinnyky - ‘the people belonging to aluan’). Strongly reduced y (like “i“ in “it“) is almost not heard, therefore it dropped out very quickly, double nn in due course gives one n, thus comes a word aluank, where the sound k is further reduced. As to the sound u, it sounds as w, and w usually sounds as a zero sound, or b, or v.
(From Alans - Türkic etymology; bold emphasis mine.)
If the sound that should cover the phonological /r/ slot is not present, tier 2 will simply indicate zero. The symbol adopted in the picture is [Ø].
(From "Diachronic change in the postvocalic /r/ in the Dutch of Amsterdam. Section 9.3.2. Zero sound and special cases", p. 29.)
This group can also yield j and zero sound, but these cases are very easy to explain and therefore will not be dealt with at length in this
(From note 1, p. 2, in "An Unknown Law of Elision in Western Romance Languages", Revista Eletrônica de Divulgação Científica em Língua Portuguesa, Lingüística e Literatura - Ano 04 n. 06-1º Semestre de 2007. See also two other instances in this article.)
... mainly to facilitate making the distinction between glottal stop and zero as in [a?e] versus [ae].
(From "Auditory vs. Articulatory Training in Exotic Sounds. Final Report", p 3.)