"My understanding is that the DSCP uses 6 bits and IP Precedence uses first 3 bits of the same 8 bit field, so even if a packet is marked EF or AF41, the ISP who uses the first 3 bits should still be able to classify this traffic as IP Prec 5 or IP Prec4 respectively."
Correct. (In fact, that's by design.)
"Is DSCP marking backward compatible with IP Precedence values ?"
Maybe, maybe not. That's an "it depends:" answer.
"I have an teams application which is tagging the Voice traffic EF and Video traffic AF41. However, our ISP uses IP precedence for QoS Queuing. I am just wondering if I would be ok to send the marked traffic as-is to the ISP or should I be re-marking it to IP precedence values 5 and 4 on the CE router ?"
Again, that's "it depends".
For example, IPPrec will "see" CS4, AF41, AF42 and AF43 all as IP Prec 4. You asked about AF41, but is there any other traffic with the other 4X (or 5x, rather than just DSCP EF) markings? Further, how will your vendor actually treat IPPrec 4 and 5, vs. how you expect DSCP AF41 and DSCP EF to be treated?
BTW, some differences between IPPrec and DSCP, when CS1 is consider "scavenger", it's treated "worse" then DSCP BE, yet IPPrec 1 shouldn't be treated "worse" than IPPrec 0. With IPPrec, priorities are ranked by ordinal value, while DSCP, CS/AF classes don't have implicit ranking, although to try to align with IPPrec, they are usually "ranked" by equivalent ordinal value.
