Type conversion in expression may affect “CardinalityEstimate” - on a computed column?
I had a look at this question:
Type conversion in expression may affect “CardinalityEstimate” in query plan choice?
But that was related to collation and not with computed columns.

It's the same issue. The warning is informational, to help you understand any issues you might notice with cardinality estimation.

Is there any way I can get rid of this warning?
Is it a persisted column, the conversion has been already done, why exactly is the query optimiser going on about it?

Just because the computed column is persisted, does not mean the optimizer will choose to use the persisted value. SQL Server routinely expands computed columns (persisted or not) into the underlying definition at the start of the compilation process. Later on, it may, or may not, match expressions back to the available persisted computed columns. When the optimizer encounters the expression, it may add a warning to the plan.
The only way to prevent this expansion and match-back is to enable trace flag 176 on suitable versions.

When I remove the MIN and MAX columns from the select, there is no more any warnings

With this change, the optimizer is able to simplify the query to remove the unnecessary join. The result is a TRIVIAL plan, with no cost-based choices, so there is no warning about plan choices.