I seem to be dealing with the same issue.

In InDesign 18.5.2 and 19.3. (macOS 13.6.4) this character is appearing in front of random footnote references after importing files from Word. It looks like a hypertext named destination, but does not respond to Delete Unused Destinations in the Hyperlink panel.

It pastes into the F/C dialog box as a hair space (Text: ^I GREP ~I) but isn't a hair space.

@Tobias Wantsen is correct: a text search for <FEFF> matches it but could be potentially disastrous in a document with other markers.

Attached two images to illustrate, and a sample file.

1.png: a Word doc showing 3 footnote references prior to import

2.png: the Word doc imported into InDesign with the : appearing in front of 2 of 3 visible footnotes in Layout view, and the bullseye/rectangle symbol appearing in front of 2 of 4 visible footnotes in Story Editor view.

EDIT: I couldn't include the sample file. You can reach out to me directly if you would like to see it.
sample.indd: 1 paragraph from that file that includes one of these characters in front of the first footnote reference.

Copy the Invisible Character , invisible letter free fire space https://psfonttk.com/invisible-character-copy-paste/

You can do a TEXT search for <FEFF> to remove it, BUT: <FEFF> is also used in the context of XML tags, notes markers, and index markers! You can’t do a search and replace without possibly messing up other functions.

InDesign CC 2019 was a revolutionary Version For me
Importing comments from a PDF file was AMAZING (I was waiting for it a long time ago), when i'm don with one of those imported comments, i deleted that comment from the panel, i discovered an unwanted hidden character with a (:) shape was left in my text, That causes me a lot of problems with the Diacritics positioning in my Text :(
I tried to remove it by copy and pasting it to the find and replace panel, it appears like a format shape ^| and it couldn't be found???!!! so I had to remove them one by one, and that means a long time when i have about 2540 comments...
Any solution for That, PLEASE...

Apply all Auto Edits inserts an invisible character before which then interferes with Find and Replace. When pasted into a GREP search, it looks like ~I, but can't be found. It can be manually removed, but this is not helpful, as I need to be able to perform a comprehensive Find/Replace.