Any person who went through 12 years of Catholic education (such as myself) would immediately recognize Alan's medal as a Sacred Heart (of Jesus) medal. Doing a quick Google search, I found a similar medal. The one pictured is described as antique French, Flaming Heart, Sacred Heart, ex voto (a religious offering given in order to fulfill a vow) medal.

I do not think it is from the Jesuits.

I did some googling on this piece utilizing terms to describe the sacred heart imagery. The trail led into "ex-voto" or "milagro" pieces associated with Mexico, Latin America, South America.

Here are a few links to pieces that resemble Alan Weinberg's. These may help with further research -- his piece may be older than these - but definitely appears to be related. I don't know if the term "ex-voto" or "milagro" is accurate for these exact pieces but it seems to be how eBay sellers are classifying them.

The badge from Alan Weinberg's collection is clearly in the tradition of Sacred Bleeding Heart of Jesus medallions. Google: "Sacred Heart" or "Sacred Bleeding Heart of Jesus" and look at the text, then at the images where one can see hundreds of such images with the exact same elements. Since I can't tell when and where it was issued one cannot preclude the possibility that Jesuits distributed it to Native Americans or Canadians but I tend to think that this is a normal Catholic devotional object rather than an Indian peace medal.

This is a relatively modern Catholic Sacred Heart medallion, likely 19th century or newer. Sometimes listed as funerary. I saw one not too long ago priced around $40-45 (unsold). See similar example at this link: https://www.pinterest.com/pin/543528248759534293/ . See also: https://larryflaxman.com/product/antique-radiant-heart-cross/