Well when someone is passing something off as 'viking' as if that denoted a people/culture/identity, there's every reason to be skeptical. There's no such thing, really, just cultures of Scandinavia in the Viking Age, which were not a monolith either.

The word "tagelharpa" (tagel meaning horse hair, referring to the string material) is modern Swedish; in Old Norse it'd have been taglharpa but doesn't exist in any Old Norse sources. "Tagelharpa" itself isn't attested until the 20th century either, it's a rendering into 'standard' Swedish of tallharpa, the name for the instrument on Ormsö (Vormsi) in the Swedish-speaking parts of Estonia. The instrument existed there, and was common in Finland and Karelia as Jouhikko or Jouhikantele which also roughly means 'horse-hair harp'. These seem to have been more popular or at least retained popularity more in Finland. It's been observed their blackened appearance is not inconsistent with the term 'soot-harp' (see below) either;

Bowed Byzantine lyres from the 12th century have been found further east in Novgorod. But the Welsh Crwth in the west, is also a similar instrument.

The oldest actual instrument in Scandinavia proper is the 'sotharpa' (soot-harp) from Öje in Dalarna, which is possibly as old as the 17th century and comes from Dalarna. (one might note that the bagpipes lived on in these parts Dalarna longer than the rest of the country as well, into the 19th century. So did runic writing)

The oldest representation of something resembling the instrument is this fellow in a carving from Trondheim cathedral (Nidarosdomen); it is dated to the mid-13th century. (There's also a bagpipe player there, which was an instrument that'd been introduced after the Viking Age)

Two theories have been proposed; (Andersson) either the Welsh instrument spreading to Norway and eastward, or the Novgorodian instrument spreading westwards; these are along well-worn trading routes both in the Viking Age but also the centuries after it. If it was Swedish settlers who brought the instrument to Estonia and Finland, it'd have more likely been after the Viking Age, in the 12-13th centuries.

I guess the short of it, is that we don't know if it existed in the Viking Age; just that it existed in Scandinavia 200 years later. It was also not a uniquely Scandinavian instrument but occurred from the Baltic region across Scandinavia to the British Isles. There's nothing saying it couldn't have existed in the Viking Age but nothing saying it did either. I'd call it a medieval instrument that might go back as far as the Viking Age.

Otto Andersson, The Bowed Harp of Trondheim Cathedral and Related Instruments in East and West, The Galpin Society Journal, Vol. 23 (Aug., 1970), pp. 4-34