Your request is defeating the purpose of IMAP which is to track what's been read versus what's not been read over multiple sources. That is, if a message has been previously "read" using IMAP, then you would want to know this, which is the purpose of IMAP in order to maintain continuity over multiple email service software (i.e. POP Peeper and the EClient, in this case).
That said, there's one thing you can do:
At the end of the day, prior to opening your EClient you can select the "read" messages you want to change to "unread" in POP Peeper and then right-click on any one of the selected messages and uncheck the option "Marked as Read" (near the top of the context-menu). This will change all of the messages you selected in POP Peeper back to "unread" (and as a result these same messages in your EClient will then be classified as "unread" as well).
Note: You can select multiple messages in the POP Peeper in-box in two ways:
1) using the "Shift" key will mark all successive messages in either direction from the first to the last message selected.
2) using the "CTRL" key you can select as many multiple messages individually as you wish.
As you can see, there are other right-click options as well as far as marking your messages in various different ways (but you have to take care as far as what your intentions are in regards to what your changing). If you are not sure about any of the other options, please feel free to ask about them before using them.
But keep in mind once again, with all of this said, your defeating the entire purpose of the tracking of messages (using IMAP) that have previously been read (via POP Peeper in this example.) The purpose of IMAP is to maintain continuity as far as what's been done over time with messages over multiple Email Services.
Again, specific to this discussion - looking back over the past history of the POP Peeper in-box messages - you're not going to know which of the messages you've previously "read" by setting the messages to "unread" (unless you're going to be reading all of the same messages over again in your EClient). In my opinion (if you stop to think about it) you're ultimately creating a catch-22 situation to address a rather minor issue in the first place.
As to your specific question, that is to quote "... prevent viewed messages in PopPeeper to be not marked as read" --
Keeping in mind there is an obvious purpose for differentiating between "read" and "unread" messages. I'm not so sure it makes much sense to actually want to "prevent" the messages you "view" in POP Peeper to ultimately never be marked as "read" (which is what you're asking) if you are using Peeper to "read messages" each day (which is presumably the case since your asking for "viewed" messages in POP Peeper to not be marked "read"). So with this in mind,
why would it make any sense for you to not know what messages have been read in POP Peeper over time?