Yes, indirectly, by reading a creature's thoughts
The detect thoughts spell allows the caster to (among other things):
learn the surface thoughts of the [target] creature – what is most on its mind in that moment.
I think it's fair to say that anything a creature is attempting to directly communicate to another creature (whether verbally or telepathically) qualifies as a surface thought and/or what is most on that creature's mind. Similarly, any communication the creature receives via the telepathic bond would likely be foremost in their thoughts at the moment it is received, unless they are very distracted (e.g. in combat), or they know that someone is attempting to read their thoughts and are making a concerted effort to avoid thinking about it.
However, one important caveat to this way of indirectly spying on the telepathic bond by reading thoughts is that you don't automatically know which thoughts are telepathic communication and which thoughts are just thoughts the creature is thinking to themselves. In most cases, it probably won't be too difficult to infer, but it's something to be aware of regardless.
Also note that Rary's telepathic bond can link more than two people. If Alice, Bob, and Claire are linked via this spell, and Alice sends a thought specifically to Bob, you probably can't read that thought in Claire's mind, unless the DM rules that the any communication through the spell is sent to all targets.
In short, I don't think there's a way eavesdrop directly on the telepathic bond itself, but there are plenty of ways to eavesdrop on the minds of those who share the telepathic bond, and this can allow you to indirectly infer what information was shared. Keep in mind that detect thoughts is only one of many ways to read minds, and each mind-reading ability is a bit different. Some more limited mind-reading abilities may not give the necessary information.