Hum, I don't think that is possible at all.
In fact, the ms-access dbase drivers don't even know of, or show deleted
records like you can in DbaseIII.
I would be both very scared, and worried if access could in fact pack those
dbase files anyway! If you connected to a slightly different version of the
dbase format file, and packed via ms-access, you likely could damage the
file. In other words, if in ms-access you choose some wrong drivers, and
they could pack the connected file, then you could destroy that file quite
easily. For this reason, and the fact of having to add this additional
functional ability to ms-access certainly explains why we can't do this from
ms-access.
On the other hand, I would be scared if ms-access could compact Oracle, or
sql server files also!
I would hope, or assume that the original software that creates that
dbaseIII data has some provisions for "pack" ing that data. If the original
software does NOT have any ability to do this, then I would consider dumping
that software as you are rapidity running out of possible solutions.
You could certainly move the data out of the dbase table, but at any rate,
ms-access never was able to pack dbase files. I certainly remember using the
pack command at the .(dot) prompt in FoxPro many moons ago...