A tiny bit of geology research Google style shows us that this material is quite similar chemically (and visually as well) to Larimar. Your gem picture made that quite clear.
Chlorastrolite and Pectolite of similar origin and chemistry. Not identical, but very close.
The mindat page Does not show these two as being related chemically but the two minerals do look a lot alike and both do have similar crystal structure at times.
Under "Relationship of Pectolite to Other Minerals" in both
Pectolite and "Relationship of Pumpellyite (Mg) to Other Species"
pumpellyite there is no correlation.
I am not able to equate the two as they form in different environments and conditions. The Pumpellyite forms in amygdules in basalt and occurs as amygdaloid structures and fracture fillings in basalt.
Pectolite forms in nepheline syenites which is a holocrystalline plutonic rock that consists largely of nepheline and alkali feldspar.
The crystallography is different for the two minerals as well with chlorastrolite having Crystal System Orthorhombic and Habit Fibrous aggregates, and Pectolite has a Crystal System Triclinic and Habit Globular masses, the rarer crystals showing tabular habit.
The habit of pectolite is especially liable to alteration, and in nature it is frequently altered to zeolites (especially natrolite), sodalite, kaolin, or compact muscovite. Another Zeolite that IS found in basalt in Michigan is Thomsonite (very similar to Chlorastrolite) and perhaps that might mean something although there is no info about one altering into the other.
I think the Larimar looks sexier though.