Inconsistency in NASA delta T on the NASA lunar eclipse page ?

[jimbabwean]

If one tests Skyfield's internal delta T against the number provided on the NASA lunar eclipse page (https://eclipse.gsfc.nasa.gov/LEcat5/LE-0599--0500.html) for the July 4th eclipse in 568 BC, it seems that there is a difference of 2 or 3 minutes between the two delta Ts. I'm not quite sure what that means, or whether I have done this correctly. Here's my test script and output from the script:

from skyfield.api import load, GREGORIAN_START

ts = load.timescale()
ts.julian_calendar_cutoff = GREGORIAN_START

ts = load.timescale()

eclipse_page_delta_t = 18123
t_unadjusted = ts.tt(-567, 7, 4, 15, 54, 22)
t_adjusted = ts.ut1(-567, 7, 4, 15, 54, 22 - eclipse_page_delta_t)

print(f'Eclipse date from eclipse page: {t_unadjusted.tt_strftime()}')
print(f'Eclipse page delta T: {eclipse_page_delta_t}')
print(f'Eclipse time calculated by skyfield: {t_unadjusted.ut1_strftime()}')
print(f'Eclipse time calculated with eclipse page delta T: {t_adjusted.ut1_strftime("%Y:%m%:%d %H:%M:%S")} UT1')

delta_t = (ts.ut1(-567, 7, 4, 15, 54, 22) - ts.tt(-567, 7, 4, 15, 54, 22)) * 24 * 60 * 60
print(f'Skyfield delta T: {delta_t:.0f}')

The output that I get is:

Eclipse date from eclipse page: -567-07-04 15:54:22 TT
Eclipse page delta T: 18123
Eclipse time calculated by skyfield: -567-07-04 10:55:13 UT1
Eclipse time calculated with eclipse page delta T: -567:07:04 10:52:19 UT1
Skyfield delta T: 17949

What does this mean?