It Cannot Be Reclaimed
In our era, beis din does not impose fines. Therefore, because of the doubt as to whether the payment is a fine or compensation, beis din does not make people who “steal” other people’s mitzvos pay anything. However, if the offended person seizes property belonging to the offender up to the value of 10 zehuvim, he is not forced to return it (Shulchan Aruch, ibid.). (Some approximate 10 zehuvim to be over $300 nowadays.)
Payment For Distress
The Chasam Sofer shares an interesting insight (Chiddushei Chasam Sofer). We know that someone who wants to fulfill a mitzvah but is forced to relinquish it is considered to have fulfilled it. If so, why must the person who stole a mitzvah from his fellow compensate him (assuming that the payment is compensation)? The offended person didn’t lose anything since he receives his reward regardless!
The Chasam Sofer explains that when a person observes a mitzvah and serves Hashem joyfully, he receives a reward for serving Hashem, whereas someone forced to relinquish a mitzvah gets a reward only for his distress. Therefore, the person who snatched the mitzvah must compensate his fellow for what he took away.