How to avoid importing duplicated transactions in Quicken
The best way to avoid duplicates is to work in the date range. If you are converting the full list of transactions for a specific date range, then delete existing transactions for the date range.
If you are importing QIF files, there is no way to avoid duplicates for existing transactions and transactions that are being imported.
If you are importing QFX (Web Connect) files, the format allows using "Unique Transaction ID" (FITID) that Quicken keeps track of for a specific account. If your bank provides these transaction IDs, then you can use them. Make sure they are truly unique, not just per file unique.
There is one issue with this: when you are converting your transactions, you may convert the same transactions several times, but Quicken keeps track of already imported transactions even if you delete them.
The converter generates unique transaction IDs to make sure when you import a QFX file, Quicken does not skip any transactions.