It would have been somewhere between 1917 and 1923, and thus the amount on that check would be the rough equivalent of getting a check for $150k-$200k today. Assuming the story is true at all, of course.
The best source we have for this story (which may well still be an Urban Myth) seems to be a letter to the Editor of LIFE magazine by a Jack B. Scott, printed in May of 1965*.
Sirs: In your article on Steinmetz (April 23) you mentioned a
consultation with Henry Ford. My father, Burt Scott, who was an
employee of Henry Ford for many years, related to me the story behind
that meeting. Technical troubles developed with a huge new generator
at Ford's River Rouge plant. His electrical engineers were unable to
locate the difficulty so Ford solicited the aid of Steinmetz. When
"the little giant" arrived at the plant, he rejected all assistance,
asking only for a notebook, pencil and cot. For two straight days and
nights he listened to the generator and made countless computations.
Then he asked for a ladder, a measuring tape and a piece of chalk. He
laboriously ascended the ladder, made careful measurements, and put a
chalk mark on the side of the generator. He descended and told his
skeptical audience to remove a plate from the side of the generator
and take out 16 windings from the field coil at that location. The
corrections were made and the generator then functioned perfectly.
Subsequently Ford received a bill for $10,000 signed by Steinmetz for
General Electric. Ford returned the bill acknowledging the good job
done by Steinmetz but respectfully requesting an itemized statement.
Steinmetz replied as follows: Making chalk mark on generator $1.
Knowing where to make mark $9,999. Total due $10,000.
We know the latest it could be is 1923 (the year Steinmetz died). If we assume this anecdote is at least correct that it had to do with River Rogue, then the earliest it could be is 1917 (the year Ford started construction on the River Rogue plant). That gives us a 6 year window, which isn't bad. If I had to guess, it would be later in the window, as they wouldn't have been trying to hook up and operate boilers before they had the buildings completed. They didn't actually start making cars there until 1928.
My handy-dandy online inflation calculator gives a value of $210,704.27 for 1917 $10k, and $142,499.42 for October 1923 $10k.
* - The article it referred to only mentions Ford going to his house to consult on an "urgent technical problem".