I would like to mark a letter in a syllable with some kind of symbol that denotes that the letter can be dropped. Is there a symbol for that in the phonetic alphabet?
The IPA doesn't have any notations that relate spelling to pronunciation, thus if [ð] can be spelled <th,dh,d>, IPA takes no note of that fact. It only deals in phonetically-interpretable segments. If some segment is present in an abstract form of a pronunciation such as an underlying form, you could indicate that using slash vs. square brackets, e.g. /ræt/ vs [ræʔ], which can imply deletion as in /pəteto/ vs [pteto].
While it is common in phonological practice to communicate "deletable segment" with parentheses, IPA assigns a different meaning to parentheses (see p. 175 of the handbook): it brackets "indistinguishable utterance". Double parentheses denote "sound obscured". There is no official IPA notation for "can be deleted".
There is no official IPA symbol for such a (non-)sound. However, language-specific phonemic transcription systems, which borrow symbols from the IPA, often use a superscript symbol for such omissible segments. So, for example, you might see the following transcription for the English word little, which can optionally be said with a schwa in the last syllable, or alternatively with a syllabic [l]:
The problem with this convention, which is the one most often found in dictionaries and so forth, is that uninitiated readers sometimes think that this indicates a 'small' sound.
The Longman Pronunciation Dictionary(LPD), the gold standard of English pronunciation dictionaries, uses this convention. Notice that due to the phonology and phonotactics of the languages concerned, such a convention often implies quite a bit more than it entails.
John Wells, world-renowned phonetician and author of the LPD writes:
The answer to the second question, too, is answered in the printed LPD. For me “əl” is an abbreviatory convention meaning “[l̩] (= syllabic l) or, less likely, [əl]”. Raised letters stand for ‘sounds optionally inserted’. So a syllabic l is one possible unpacking (the most likely one) of superscript schwa plus l. (You can tell it must be syllabic, because the syllables are shown by the spacing and there are no (other) vowels in the syllable.) By writing “ˈʃmaɪkəl” I am indicating “ˈʃmaɪk l̩ or (less likely) ˈʃmaɪk əl”. The raised-letter convention saves space. I do the same thing in words such as fence fents.
[To find the relevant section, scroll down to 'Dictionary Conventions', blog section Wednesday 22 November 2006]