I always thought Anjuli in the Indian context was a variant of Anjali; in fact, I have never seen Anjuli in India because the tendency in most places in India would be to pronounce it with the -u- as in English put if spelt that way. The actual pronounciation in Sanskrit had the indeterminate vowels schwa (the a in English about, for example) at both positions. The stress on the last short i is not heard in modern Indian languages. the n is soft and palatal that is heard in some Spanish words, the j and l are like English.
As to the meaning, the database here, not surprisingly, has it right. The root is anj, cognate with and meaning the same as the root of unguent. From that anjali meant the hands to soothe or spread with etc., but it is used in the specific context of the two hands held together with the palms together forming a shallow cup. This was a common gesture for both granting and for supplication, and the word could be used for both. In modern Indian languages, the most common association is with offerring flowers to the gods which are dropped (never thrown) from cupped hands; and by metonymy refers to the thing offerred, though, especially in north Indian languages, it is still recognizably a metonymy.