Check out the 10th Michigan Cavalry.

I would very much be suprised if Federal soldiers, individually discharged, were not issued vouchers for
train travel.

Up to the spring of 1865 only the rail line from Knoxville North to Bristol were not in their hands.

At the most, I would expect Federal troops would not have had to go no further on foot West
to Nashville and then board the cars. However, they could have reached there by way of Chattanooga.

At the end of the war, Federal troops controlled all the rail lines out of Knoxville.

.......

10th Michigan Cavalry

the Tenth
returned to East Tennessee on the 31st day of May, having
marched not less than 1,800 miles in the enemy's country,
without any base of supplies, living on the country, except for
the few days' rations received from Atlanta, for 58 days,
counting from the end of the eight days for which rations were
issued on the 26th of March. Much to the disappointment of the
men, the regiment was not to be mustered out at once. There
was a reorganization of the Division at Linoir Station.
Colonel Trowbridge was assigned to the command of the First
Brigade, and Major Standish to the regiment, Lieutenant Colonel
Smith being still on staff duty at Headquarters in Knoxville.
This assignment continued at Lenoir Station and Sweetwater
until the latter part of August, when the Tenth was ordered to
Jackson, West Tennessee. Colonel Trowbridge's term of
enlistment would expire on the 1st of September, and he thought
as the war was over it would be but fair for him to muster out,
and thus make possible a promotion in each grade. By
permission he remained at Knoxville until he mustered out on
September 1st. On August 24th the regiment, under commend of
Lieutenant Colonel Smith, left for Jackson, West Tennessee.
Captain Light had returned, having had great success in
recruiting, and the ranks were full enough to permit promotion
and muster in all the grades. The regiment remained in West
Tennessee until the latter part of October, when it was ordered
to Jackson, Mich., where on November -- it was finally mustered
out and paid off.

Source: Record of Service of Michigan Volunteers
in the Civil War 1861-1865 (vol. 40)