I have received a little more information on the blazons from seeing the wood panels in Solihull.
It appears Alice is using the same arms as used by Thomas Greswold, Esquire, who dies in 1577 (Her uncle)
The Wood panel in Solihull church gives Alice's arms as -
1. Greswold - Argent, a fess gules and in chief two greyhounds courant sable.
2. Hawes - Azure, a chevron argent between three leopards faces or.
3. Blacklowe/Blakelowe or Hugford
- Azure?, a chevron between three garbs (Closed Cups?) or.
4. ? - Azure, a chevron argent between three pheons reversed or.
I so far cannot find any instance of a Greswold male marrying a Hawes or Blacklowe but these 2 arms are seen in the Visitation of Warwickshire.
The arms of the 3rd quartering on the wood panel are described as 'Garbs' by whoever blazoned them on the document I possess. From looking at the picture of the board they could possibly be closed cups, if so these are the same arms as the Hugford family of Solihull. This maybe the correct identification as the Greswold family pedigree is topped by 'John Greswold of Kenilworth, Warwickshire who marries a daughter of William Hugford of Hulverle Hall, Solihull.
I do not know who the last Arms belong to.
The Hawes are a well known land owning family around Solihull and via the Greswold pedigree, a daughter of John Greswold of Kenilworth married Thomas Hawes of Shirley in the early 1300s.
The pedigree also shows Alice's grt grandfather John Greswold of Longdon Hall as marrying an Elizabeth unknown (Could possibly have been a Hawes)
Alice's uncle is using the same arms so this perhaps shows that these quarterings were in use prior to Alice, I don't think she would have inherited them from him as she was not heir of her uncle and he had male issue. She was only heir of her brother Richard who died without issue in 1555.