The TrueType fonts included with Esri software are either created by Microsoft and supplied with the Windows operating system and then licensed by third-parties or created by Esri. Esri has limited rights to use those fonts licensed from Microsoft or owns those created by Esri.
Alphabet fonts themselves are generally not subject to copyright although the software that renders the fonts may be. However, where 'scalable fonts' are at issue, these may be subject to copyright depending on the degree of creativity in them. For example, standard Times Roman, Garamond, and Arial are probably not subject to copyright protection but a custom designed Olde English style or specially designed symbols might be.
The significance of whether or not a font is subject to copyright law is that works subject to copyright are essentially 'owned'. Any modification of a copyrighted work is considered to be a 'derivative work' to the original work, and is therefore also owned by the copyright holder. In this case, if the font symbols are subject to copyright law, the modifications are derivative works and are therefore also owned by Esri and cannot be used or redistributed or otherwise transferred without Esri’s express consent such as with a use license.
In addition, a specially created font, alphabet, or symbol may also be subject to trademark protection.
Setting the copyright and trademark question aside, your inquiry presupposes that Organization A is licensed to use Esri software, presumably under Esri’s standard Master License Agreement that requires the technology to be used 'as a single package'. Thus, both modifying or redistributing the Esri TrueType Symbol Fonts would violate the license terms.
Q: Does Organization A own the modified fonts?
A: No. Even assuming that Organization A does have a valid license to use Esri software, if the fonts are copyrightable, Organization A still does not own the modified fonts because they are a derivative work of copyrighted material and are owned by Esri. In addition, even if the fonts are not copyrightable, under Esri’s license by which Organization A is presumably bound; they may not take a font, modify and redistribute it because it violates the use “as a single package” clause.
Q: Is Organization A breaking copyright by giving them to Organization B?
A: Yes. If the fonts are copyrightable then there are two violations of the copyright law. First, creating the modifications would be a violation of the copyright law that grants the copyright owner, Esri, the exclusive right to modify the work, i.e. prepare derivative works. Second, Esri would own the modifications and therefore distributing them to Organization B would also be a violation of the copyright law. Subsequent distributions are equally in violation.
Q: Can Organization A give the fonts to Organization C who owns Esri products and thus has the unmodified fonts?
A: Not without Esri’s permission. First, organization C would be a licensee of Esri software with specific use rights. They would not 'own' Esri software. Again, Organization A cannot permit use of the modifications by anyone, at any time, without Esri’s permission, which, incidentally, under Esri policy would need to be in writing authorized by a corporate officer or director.
Q: Can Organization A serve the fonts on a website for the public to download?
A: No. As discussed above, if the fonts are subject to copyright, it is Esri’s exclusive right to use and license them, including putting them on a web site. Even if the fonts are not subject to copyright, such use violates Esri’s license agreement.
Esri is open to permitting creation and use of modifications that do not negatively impact its business model. We would need to review any such modifications on a case-by-case basis. We look forwarded to discussing possible use resolutions to allow the modifications to be used and distributed while protecting everyone’s interests.
Q: Do the copyright restrictions apply to Esri fonts embedded in a PDF?