Without rewriting this query, is there a way to force the query optimizer to better estimate the amount of resources required, e.g. with query hints?
This query, as written, must compare every pair of rows, and the cost estimate is reasonably accurate.

On a supported version of SQL Server you might get a parallel plan, or there is an undocumented query hint that will force a parallel plan.

select t1.itemid, t2.itemid
from #temp T1  
inner join #temp as t2
  on t1.itemid like '%' + t2.itemid + '%'
  and t2.itemid &lt;&gt; t1.itemid
OPTION(USE HINT('ENABLE_PARALLEL_PLAN_PREFERENCE'))