I intended to look up the notation for both and compare them, but when I lookt up the notation for Op. 71: VII, I noticed an asterisk after the title:
which lead to a footnote at the bottom of the page:
I'm glad that footnote was there because the notation is still above my skill level. I did notice though that Arietta and Remembrances are both in the same key: Eb major.
Most of the books of Grieg's Lyric Pieces that I have are incomplete; I have only excerpts. This is the case with Book X. I lookt up the complete book and discovered that Remembrances is the last piece in the book. Since Book X is also the last book of Grieg's Lyric Pieces, there's a sort of bookending going on. He starts and ends his Lyric Pieces with a similar-sounding tune.