Welcome to this user forum. @NicoleOne
You need to have a signal level between 70-95% and a quality of 100%.
Too little or too much signal can cause problems.
The strength is 100% but the quality is poor through the box.
But the quality is perfectly fine when the aerial is connected to the TV.
Are there known issues with the BT TV boxes?
If its 100%, then it a good chance there is too much signal, and its overloading., that will cause a poor quality picture.
The YouView boxes are quite fussy about the signal level, and reducing it slightly to about 85-90% may overcome the problem as it does not seem to be too weak, but it could be too strong.
A signal reduction can be made using a variable attenuator like this.
If you search sites like Amazon, for LOOPS Aerial Coaxial Cable Variable Attenuator, or Philex Variable TV Signal Attenuator