According to this site:
Special Instructions [IPTC Core] Alternative label from older IPTC IIM schema, used for "Instructions."
Instructions [IPTC Core] This is a simple text field that can include any of a number of instructions from the provider or creator to the receiver of the photograph. Any of the following might be included: embargoes (eg: News Magazines OUT) and other restrictions not covered by the Rights Usage Terms field (or new PLUS rights related fields); information regarding the original means of capture (scanning notes, color profile, etc.) or other specific text information the user may need for accurate reproduction; additional permissions or credits required when publishing. Note: This field is “shared” with the “Instructions” field in the Origin panel of the Adobe Photoshop File Info dialogue.
Examples: *Image to be used one time only, non-exclusive in English-language-edition magazine as inside image, no larger than a full page in color. Additional third-party rights to be negotiated with Julie Doe / XYZ Agency in advance. All rights not specifically granted are reserved. See delivery memo for specific license.
For consideration only; no reproduction in any form without prior, written permission.*
That's the International Press Telecommunications Council (IPTC) standard Information Interchange Model (IIM).
I haven't been able to decode Facebook's data, but pasting, downloading, and pasting an image again will change the data slightly.
Using IrfanView to set special instructions to "testing" in a JPG without IPTC data, adds these bytes to the header:
I've downloaded 339 images with instruction length 94 after the FBMD, and the following bytes stayed the same:
0 {'0': 339} 1 {'1': 339} 2 {'0': 339} 3 {'0': 339} 4 {'0': 339} 5 {'a': 339} 8 {'0': 339} 9 {'3': 339} 10 {'0': 339} 11 {'0': 339} 12 {'0': 339} 13 {'0': 339} 18 {'0': 339} 19 {'0': 339} 20 {'0': 339} 21 {'0': 339} 26 {'0': 339} 27 {'0': 339} 28 {'0': 339} 29 {'0': 339} 34 {'0': 339} 35 {'0': 339} 36 {'0': 339} 37 {'0': 339} 42 {'0': 339} 43 {'0': 339} 44 {'0': 339} 45 {'0': 339} 50 {'0': 339} 52 {'0': 339} 53 {'0': 339} 58 {'0': 339} 60 {'0': 339} 61 {'0': 339} 66 {'0': 339} 68 {'0': 339} 69 {'0': 339} 74 {'0': 339} 76 {'0': 339} 77 {'0': 339} 82 {'0': 339} 84 {'0': 339} 85 {'0': 339} 90 {'0': 339} 92 {'0': 339} 93 {'0': 339}
I also found 3 images with only 86 mystery bytes after FBMD, e.g. 23000986030000f91d0000e5230000502900004889000041ac000004c900007aee0000cf0f0100f02d0100, also saved in the past few months. Same bytes there were:
0 {'2': 3} 1 {'3': 3} 2 {'0': 3} 3 {'0': 3} 4 {'0': 3} 5 {'9': 3} 6 {'8': 3} 8 {'0': 3} 9 {'3': 3} 10 {'0': 3} 11 {'0': 3} 12 {'0': 3} 13 {'0': 3} 16 {'1': 3} 18 {'0': 3} 19 {'0': 3} 20 {'0': 3} 21 {'0': 3} 26 {'0': 3} 27 {'0': 3} 28 {'0': 3} 29 {'0': 3} 34 {'0': 3} 35 {'0': 3} 36 {'0': 3} 37 {'0': 3} 42 {'0': 3} 43 {'0': 3} 44 {'0': 3} 45 {'0': 3} 50 {'0': 3} 51 {'0': 3} 52 {'0': 3} 53 {'0': 3} 58 {'0': 3} 59 {'0': 3} 60 {'0': 3} 61 {'0': 3} 66 {'0': 3} 67 {'0': 3} 68 {'0': 3} 69 {'0': 3} 74 {'0': 3} 76 {'0': 3} 77 {'0': 3} 82 {'0': 3} 84 {'0': 3} 85 {'0': 3} 86 {'\x00': 3}
This blog post appears to know more about it:
[...] on 2014-11-13, Facebook introduced a new tracking code. It appears as an IPTC Special Instructions metadata field. They look like:
Special Instructions: FBMD01000ac60300004a1d00002d4b000067580000c9650000d5fc000054350100953a0100d3420100e84b01005f8f0100
Special Instructions: FBMD23000969010000b1590000cb7700000a8600000c07010046820100b8c0010052590200e5c902006e440300
I think that "FBMD" stands for "Facebook Member Data" (but I could be wrong).
I've manged to decode one interesting aspect in these strings: the length. Each string starts with "FBMD", two hex characters (1 bytes), and a 16-byte (4-character) length. Then comes length+1 sets of 32-bit (8-byte) values.
FBMD01 000a = length 10, so expect 11 fields: c6030000 4a1d0000 2d4b0000 67580000 c9650000 d5fc0000 54350100 953a0100 d3420100 e84b0100 5f8f0100
FBMD23 0009 = length 9, so expect 10 fields: 69010000 b1590000 cb770000 0a860000 0c070100 46820100 b8c00100 52590200 e5c90200 6e440300
I've asked the Facebook community about it.