Hi Mark,
Thanks for your interest in Syncfusion products.
I am afraid that I am not able to reproduce the issue of unbound column with custom item templates . The item templates do not disappear after triggering callback through search function. Also created a sample to test this issue and please refer the sample in the link below:
http://websamples.syncfusion.com/samples/Grid.Web/6.2.0.40/Grid_ASP_unbound/main.htm
Please try running the sample and if still the issue exists, could you please try reproducing it in the above sample so that we can analyse further and sort out the cause to provide you a solution?
Thanks,
Janagan.