How do I check the exchange rate without confusing it with transaction fees?

Use the gross conversion figures first. Compare the foreign amount converted with the gross INR amount before fees and tax. The rate implied by those two figures is different from the effective rate you get by dividing the final net bank credit by the foreign amount.

Skydo's homepage example lists a transaction fee and GST after the conversion value. Those deductions reduce the net INR credit even when the conversion uses the stated rate. If your payment record does not give enough detail to separate these items, ask support@skydo.com for the applied rate, gross INR, fee, tax and final settlement amount for that reference.