I believe MilkailovskyVV is correct with the solution. Let me explain why I think you are seeing this. Below is your basic routing config for each router
router eigrp 1
network 18.104.22.168 0.0.0.255
router bgp 2
network 22.214.171.124 mask 255.255.255.0
neighbor 126.96.36.199 remote-as 2
neighbor 188.8.131.52 update-source Loopback0
neighbor 184.108.40.206 remote-as 2
neighbor 220.127.116.11 update-source Loopback0
neighbor 192.168.10.1 remote-as 1
Since auto-summary is on under EIGRP, the 18.104.22.168 /24 network will be auto-summarized across different major networks. It is passing between 192.168.X.X, so it will be summarizzed. Therefore, your routers will see 22.214.171.124/8.
Now here comes BGP. Your neighbors are linked to the loopback interface. In this example your 2.2.2.X Interface. Initially, your BGP comes up, but then it see's your advertisement "network 126.96.36.199 mask 255.255.255.0". Now your router will have two entries in the routing table, one from EIGRP (188.8.131.52 /8), and one for BGP (184.108.40.206 /24). Which route will it use to try and communicate with your BGP neighbor? The most specific, which happens to be advertised by the BGP neighbor. So you have the router trying to get to 220.127.116.11/24 by 18.104.22.168, this is where the recursive lookup comes from, it no longer is looking at the EIGRP route, since the one via BGP is more specific. Hope this makes sense.
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