That there is a semantic link in Q(u)enya between the act of thanking and giving, and that a similar link exists in Hebrew, makes sense. (Although the link is not universal; English thank is linked to think, and in Hungarian köszön has the meaning "thank" and "greet".

What's rather interesting to me that this rather common and important verb is so scarcely attested in the Elvish corpus; as far as I know even the usually so helpful and rich Gnomish corpus does not contain anything like it; all we have is Eruhantale and the root HAN as glossed in VT43. We don't even know whether Tolkien had *hantale in mind when he glossed HAN (although it is certainly possible).

In Polish DAwać means 'to give', odDAnie - 'devotion' and przyDAwać - increase - very elvish :-). 

I've got a crazy idea: is it possible that there is only one verb anta- meaning both 'give' and 'thank', and h in eruhantale is only intrusive consonant put there to avoid hiatus?

+Remi Korben He wrote Eruontari 'Mother of God_ around the same period (second half of 50s), so — no. The thing is, Tolkien changed his mind about the initial H of Eldarin. When he introduced that basic element in a revision to Outline of Phonology he made it remain in Q and vanish in all Telerin; however, in QE it already remains consistently both in Q and T. There is little doubt that when writing Eruhantale in ca. 1959 (and maybe even when retyping it in 1965) he had no problems with its derivation from HAN and sufficient difference from anta which was consistently from AN 'allative' since the Etym., except maybe the obvious semantic parallel. The waters have muddled when Tolkien started seriously considering around 1968 (and often assuming as a fact) that H remains in Telerin only. See HENET, hor etc. in Notes on Óre discussion, PE22 and similar. (However, he did not make a conscious shift! In LVS13 he reminds himself that H in Quenya does remain [to disobey himself in the next phrase]. He just wanted more sources for Q vocalic beginning — and got them. A parallel problem was that he noticed: _anta_could only mean something like 'send' if treated lightly; so in mid-60s he reshapes it from AM (Comparative in Eldarin), and in 1969 apparently forgets that.
Actually, I keep believing in H remaining (too many things crumble without that) and hence in hanta 'thank' separate from anta < amta 'give'. Sindarin might be antha, anthant for former and antha, aun for latter; or even antha, anthant vs. an, aun which I favour. After all, in the batch of Comparative, and, Ambar Tolkien allows himself many minor abandoned controversies in commentary, such as suddenly making men 'go, proceed' into menta for no reason and eliminating any word for 'send' by wiping anta simultaneously. Hence — I do take his anha there lightly, as a remnant of a previous concept.

Still, there are Sindarin words beginning in ha- still. Is it only in this particular case initial "h" disappears?

+Hjalmar Holm That's not the point. Sindarin initial h is only from KH and SK and was like that as early as the Comparative Tables.