Remarkedly is a word.
The Oxford English Dictionary classifies the word as a derived form of "Remarked, adj. 1":
Marked, conspicuous, noted, notable. Now chiefly with modifying adverb.
For the adverb, the OED collects several examples starting from the 17th century:
1656 N. Stephens Plain Calculation Name & Number of Beast 181 The time when this Universal [Papal] Headship began visibly and remarkedly to appear, this is The Number of the Beast, and more specially of his Name and Headship.
1855 Putnam's Monthly Mag. Apr. 403/2 The species extends over the whole country, and in the South, where it attains its greatest size, it is remarkedly distinct from the lanceolata.
1871 S. Mateer Travancore 363 The discipline and general good deportment which is remarkedly observable in you.
1985 J. Kerman Musicol. 45 Manfred Bikofzer had a remarkedly clear head for historical generalization.
2007 Sunday Herald (Glasgow) 24 June 14/3 Remarkedly free with swearie words.
It's possible that modern usages are an error that comes from mixing up remarkably and markedly. That is hard to categorize though, and the possibility of error shouldn't be taken to suggest that remarkedly isn't a word. In the Corpus of Contemporary American English, I found this example from a 1990 PBS Newshour interview (4/30/1990) between the host, Mr. Lehrer, and then-Undersecretary of State for Political Affairs, Mr. Kimmitt, where the latter uses remarkably and remarkedly in close succession:
I don't have any details on it. I would say that I have seen the same television pictures as you. I thought that he looked remarkably well and remarkedly well composed for a man who had been in captivity for almost four years.
Was he reduplicating the re- on the second utterance in error, intending markedly, or choosing remarkedly as a distinct echo of the first? There's too little information to know for sure what Mr. Kimmitt intended, so we have to judge based on what he actually said.
Given that it is used, and is defined and attested for some time, it makes sense to treat it as a distinct word with similar meaning to markedly or remarkably.