How to remove files from a sparsebundle file (previous Time Machine image)?
So the comment @GordonDavisson gave above got me thinking about permissions and with a little extra searching I ended up finding this answer to  How can I delete Time Machine files using the commandline

I ended up doing the following

% du -sh geek-imac.sparsebundle
711G    geek-imac.sparsebundle

% hdiutil attach geek-imac.sparsebundle
/dev/disk3              GUID_partition_scheme           
/dev/disk3s1            EFI                             
/dev/disk3s2            Apple_HFS                       /Volumes/Time Machine Backups

% cd &lt;to appropriate folder&gt;

% sudo /System/Library/Extensions/TMSafetyNet.kext/Contents/Helpers/bypass rm -rf *.m4v

%  hdiutil detach disk3
"disk3" unmounted.
"disk3" ejected.

% hdiutil compact geek-imac.sparsebundle
Starting to compact…
Reclaiming free space…
............................................................................................................................................................................................................................................
Finishing compaction…
Reclaimed 172.2 GB out of 1.3 TB possible.

% du -sh geek-imac.sparsebundle
539G    geek-imac.sparsebundle


I had not heard of bypass before, but will keep it in my toolbox for future work.