This item is listed in my Michel postal stationery catalogue as EU3, five pence violet. The EU stands for Einschreibeumschlage which means printed envelope. These were the first postal stationery items to be issued by the newly independent "Irish Free State" as Ireland was known then. It was issued in 1924, and there seem to have been three variants. My knowledge of German is extremely limited but it seems to depend on the distance between the 'r' and the 'a' in the word Claratact, and whether the text Armstrong + Co. Dublin appears on the envelope. This conforms with the standard for registered envelopes in the UK, and, apparently in Ireland as well, in that the postal fee is higher than the normal first class rate and there is a cross in blue printed on the envelope. The envelopes also came in different formats depending on size, with the smallest, which is what yours appears to be, being 134 X 83 mm. The price in 1986, the year of my catalogue was either 140, 70 or 55 Deutschmarks, so a fairly good price even then. The 55 DM is for the one with "Armstrong + Co." and I don't see that on yours so it could be one of the two higher priced ones.
Am I correct that the envelope is a bi-layer inner-cloth and outer-paper?
From the US registry postmarks on the reverse side, it clearly was handled as registered, however it seems to be lacking the registry number label which would have been on the front, at upper left covering the "This space is reserved ..." message.