Keep in mind that Wi Fi signals are extremely weak, so for anyone else to make use of yours, that person and the pirate PC would have to be very close to your premises.
That low Wi Fi signal strength is demonstrated by the very fact that you have invested in the Wi F Extender, to operate within your own premises.
If you have a portable Wi Fi PC or similar, try going outside and around the perimeter of your house, to discover the limits of operation. Probably about 50 feet (16 Metres).
Most present Wi Fi circuits operate in the 2.4 Gbps radio-frequency band, chosen for amongst other reasons as one which is readily attenuated/absorbed by structures and atmospheric water, thus covers short distances only.
Baby monitors, micro-wave cookers etc also operate in this UNLICENCED Band.
I have just checked on my EE/Orange Brightbox Router. It has a section "Currently Connected Devices", there being four at presnt-
My PC Tower (named) by LAN (Ethernet Cable)
My lady-wife's Laptop (named) by Wi Fi
HP Printer ("Unknown Device") by Wi Fi
Samknows Monitor ("Unknown Device") by LAN (Ethernet Cable)
Also given are the local IP Address of each one - but as this is locally generated, it does not convey much; and the MAC Address of each device, which is more significant, but normally of little practical use.
By switching likely "Unknown Devices" Off and then On, you can identify/locate them. This may take a minute or more for each device.
If you download a Wi Fi Monitoring program such as inSSIDer on to a Wi Fi connected PC (typically a Laptop), you will be able to "see" other Wi Fi circuits in the neighbourhood.
This will help supplement your knowledge of how far your own Wi Fi signals can be "seen".
If your Router is also part of the BT FON arrangements and similar then there is a greater chance that others are legitmately logging in via your Router, as that is part of your Contractual Agreement with BT.
I do not know the full details of that Agreement; nor how those legitimate users show up on your Router, perhaps someone could enlighten us?